matlab

2011-2012

Universitatea Tehnică „Gheorghe Asachi” din Iaşi

Facultatea de Construcţii şi Instalaţii

METODE AVANSATE ÎN CALCULUL

STRUCTURILOR

LUCRAREA II

Masterand Solonaru Maria

Reabilitarea şi Creşterea Siguranţei Construcţiilor

Metode avansate în calculul structurilor

Solonaru Maria

PROBLEMA NR. 1- GRAFICUL UNEI FUNCŢII COMPUSE

Graficul unei funcţii compuse

1. Enunţul problemei

Să se realizeze graficul unei funcţii compuse date în programul de calcul Matlab.

2. Analiza problemei

Date de intrare: x

Date de ieşire: y

Formula lui Heron:

𝑦 = sin 2𝑥 + cos(𝑥

2) ,

3. Programarea problemei

Pentru rezolvarea problemei s-a folosit programul de calcul Matlab.

% Masterand Solonaru Maria, RCSC % acest program este unul de test grafic clear all close all % mesaj introductiv disp('Graficul unei functii compuse') %generarea argumentului functiei x=0:0.001:10; mx=x(end); %generarea valorilor functiilor y=sin(2*x)+cos(x/2); %calculul maximului si a minimului [ymax,imax]=max(y); [ymin,imin]=min(y); %generarea figurii 1 h11=figure(1); set(h11,'color',[1 0.8 0.8]) h12=plot(x,y,[0 mx],[0 0]); set(h12(1),'color',[1 0.3 0]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.5 0.3 0.5]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('FUNCTIE COMPUSA, Solonaru Maria'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[1 0.5 0]) h14=xlabel('Argumentul functiei, x'); set(h14,'fontname','times','fontsize',16) set(h14,'color',[0.8 0.3 0.6]) h15=ylabel('Valoarea functiei, f(x)'); set(h15,'fontname','times','fontsize',16) set(h15,'color',[0.8 0.3 0.6]) set(gca,'color',[0.5 1 0.8]) h16=text(x(imax+300),0.95*ymax,['maxim=',num2str(ymax),' pentru x=',num2str(x(imax))]) set(h16,'fontweight','bold')


Solonaru Maria

h17=text(x(imin+300),0.95*ymin,['minim=',num2str(ymin),'pentru x=',num2str(x(imin))]) set(h17,'fontweight','bold') set(h11,'Position',[150 50 600 500])

4. Rezultate

PROBLEMA NR. 2 - SEISME

Seism 1 : Vrancea, 4 martie 1977


Să se traseze graficele înregistrării seismului din Vrancea, 4 martie 1977, pentru

componentele nord-sud, est-vest şi vertical, pentru pasul de timp 0.02.



%Masterand Solonaru Maria, RCSC, an I clear all close all disp('grafic cutremur VRANCEA') load VRAN.ACC [n,m]=size(VRAN); timp=0:0.02:(n-1)*0.02; nordsud=VRAN(:,2); [y1max,i1max]=max(nordsud); [y1min,i1min]=min(nordsud); estvest=VRAN(:,1); vertical=VRAN(:,3);


Solonaru Maria

h11=figure(1) set(h11,'color',[0.3 1 0.3]) set(h11,'name','Masterand Maria Solonaru, RCSC, an I') h12=plot(timp,nordsud,[0 timp(end)],[0,0]) set(h12(1),'color',[1 1 0]) set(h12(1),'linewidth',[0.5]) set(h12(2),'color',[0.5 0.6 1]) set(h12(2),'linewidth',[0.5]) set(h12(2),'linestyle','--') h13=title('Seism Vrancea, nord-sud'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[1 0.5 0]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.5 0.9 1]) h21=figure(2) set(h21,'color',[0.7 0.3 1]) set(h21,'name','Masterand Maria Solonaru, RCSC, an I') h22=plot(timp,estvest,[0 timp(end)],[0,0]) set(h22(1),'color',[0.3 0.6 0.9]) set(h22(1),'linewidth',[0.5]) set(h22(2),'color',[0.7 0.6 0.5]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Seism Vrancea, est-vest'); set(h23,'fontname','times','fontsize',18) set(h23,'color',[1 0.5 0]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.5 0.9 0.8]) h31=figure(3) set(h31,'color',[0.5 0.5 0.5]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(timp,vertical,[0 timp(end)],[0,0]) set(h32(1),'color',[1 0.9 0.9]) set(h32(1),'linewidth',[0.5]) set(h32(2),'color',[0.2 0.3 0.8]) set(h32(2),'linewidth',[1]) set(h32(2),'linestyle','--') h33=title('Seism Vrancea, vertical'); set(h33,'fontname','times','fontsize',18) set(h33,'color',[0.7 0.1 0]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.2 0.2 0.8]) h41=figure(4) set(h41,'color',[0.9 0.9 0.2]) set(h41,'name','Masterand Maria Solonaru , RCSC, an I') subplot(3,1,1) plot(timp,nordsud) subplot(3,1,2)


Solonaru Maria

plot(timp,estvest) subplot(3,1,3) plot(timp,vertical)

3. Rezultate

Seism 2 : Kobe, 17 ianuarie 1995


Să se traseze graficele înregistrării seismului din Kobe, 17 ianuarie 1995, pentru





Solonaru Maria

% Masterand Solonaru Maria clear all close all disp('Grafic cutremur Kobe') load KOBE.ACC [n,m]=size(KOBE); timp=0:0.02:(n-1)*0.02; nordsud=KOBE(:,2); [y1max,i1max]=max(nordsud); [y1min,i1min]=min(nordsud); estvest=KOBE(:,1); vertical=KOBE(:,3); h11=figure(1) set(h11,'color',[0.5 0.4 0.1]) set(h11,'name','Masterand Maria Solonaru, RCSC, an I') h12=plot(timp,nordsud,[0 timp(end)],[0,0]) set(h12(1),'color',[1 0.1 0.5]) set(h12(1),'linewidth',[0.5]) set(h12(2),'color',[0.5 0.9 0.5]) set(h12(2),'linewidth',[0.5]) set(h12(2),'linestyle','--') h13=title('Seism Kobe, nord-sud'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[1 0.5 0.1]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.5 0.9 0.8]) h21=figure(2) set(h21,'color',[0.5 1 0.7]) set(h21,'name','Masterand Maria Solonaru, RCSC, an I') h22=plot(timp,estvest,[0 timp(end)],[0,0]) set(h22(1),'color',[0.3 0.5 0.9]) set(h22(1),'linewidth',[0.5]) set(h22(2),'color',[0.7 0.1 0.5]) set(h22(2),'linewidth',[0.5]) set(h22(2),'linestyle','--') h23=title('Seism Kobe, est-vest'); set(h23,'fontname','times','fontsize',18) set(h23,'color',[1 0.5 0.3]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.1 0.9 0.2]) h31=figure(3) set(h31,'color',[0.8 0 0.2]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(timp,vertical,[0 timp(end)],[0,0]) set(h32(1),'color',[0 0 1]) set(h32(1),'linewidth',[0.5]) set(h32(2),'color',[1 0.1 1]) set(h32(2),'linewidth',[1]) set(h32(2),'linestyle','--') h33=title('Seism Kobe, vertical'); set(h33,'fontname','times','fontsize',18) set(h33,'color',[1 0 0])


Solonaru Maria

ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.5 0.1 0.1]) h41=figure(4) set(h41,'color',[0.9 0.1 0.2]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') subplot(3,1,1) plot(timp,nordsud) subplot(3,1,2) plot(timp,estvest) subplot(3,1,3) plot(timp,vertical)

3. Rezultate


Solonaru Maria

Seism 3 : El Centro, 18 mai 1940


Să se traseze graficele înregistrării seismului El Centro din 18 mai 1940, pentru

componentele nord-sud, est-vest şi vertical cu pasul de timp 0.02.



% Masterand Solonaru Maria, RCSC, an I clear all close all disp('grafic cutremur EL CENTRO') load ELCTR.ACC [n,m]=size(ELCTR); timp=0:0.02:(n-1)*0.02; nordsud=ELCTR(:,1); [y1max,i1max]=max(nordsud); [y1min,i1min]=min(nordsud); estvest=ELCTR(:,1); vertical=ELCTR(:,1); h11=figure(1) set(h11,'color',[0.3 0 0.7]) set(h11,'name','Masterand Maria Solonaru, RCSC, an I') h12=plot(timp,nordsud,[0 timp(end)],[0,0]) set(h12(1),'color',[0.1 0.1 0.1]) set(h12(1),'linewidth',[0.5]) set(h12(2),'color',[0.3 0.6 0.9]) set(h12(2),'linewidth',[0.5]) set(h12(2),'linestyle','--') h13=title('Seism El Centro, nord-sud'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[1 0.5 0.1]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.5 0.1 0.4]) h21=figure(2) set(h21,'color',[0.8 0.1 0.7]) set(h21,'name','Masterand Maria Solonaru, RCSC, an I') h22=plot(timp,estvest,[0 timp(end)],[0,0]) set(h22(1),'color',[0.1 0.5 0.9]) set(h22(1),'linewidth',[0.5]) set(h22(2),'color',[0.2 0.6 0.5]) set(h22(2),'linewidth',[0.5]) set(h22(2),'linestyle','--') h23=title('Seism El Centro, est-vest'); set(h23,'fontname','times','fontsize',18) set(h23,'color',[0.9 0.8 0.3]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1;


Solonaru Maria

axis(ax); set(gca,'color',[0.8 0.3 1]) h31=figure(3) set(h31,'color',[0.9 0.7 0.1]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(timp,vertical,[0 timp(end)],[0,0]) set(h32(1),'color',[1 0.3 0.7]) set(h32(1),'linewidth',[0.5]) set(h32(2),'color',[0.7 0.9 0.8]) set(h32(2),'linewidth',[1]) set(h32(2),'linestyle','--') h33=title('Seism Kobe, vertical'); set(h33,'fontname','times','fontsize',18) set(h33,'color',[1 0 0]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.5 0.4 0.8]) h41=figure(4) set(h41,'color',[0.6 0.7 0.2]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') subplot(3,1,1) plot(timp,nordsud) subplot(3,1,2) plot(timp,estvest) subplot(3,1,3) plot(timp,vertical)

3. Rezultate


Solonaru Maria

Seism 4 : Time


Să se traseze graficele înregistrării seismului Time, pentru componentele nord-sud, est-vest şi

vertical, pentru pasul de timp 0.02.



% Masterand Maria Solonaru, RCSC, an I clear all close all disp('grafic cutremur TIME') load TIME.ACC [n,m]=size(TIME); timp=0:0.02:(n-1)*0.02; nordsud=TIME(:,1); [y1max,i1max]=max(nordsud); [y1min,i1min]=min(nordsud); estvest=TIME(:,1); vertical=TIME(:,1); h11=figure(1) set(h11,'color',[0.3 0.8 0.3]) set(h11,'name','Masterand Maria Solonaru, RCSC, an I') h12=plot(timp,nordsud,[0 timp(end)],[0,0]) set(h12(1),'color',[0.4 0.9 0.1]) set(h12(1),'linewidth',[0.5]) set(h12(2),'color',[0.3 0.7 0.1]) set(h12(2),'linewidth',[0.5]) set(h12(2),'linestyle','--') h13=title('Seism Time, nord-sud'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0.8 0.2 0.6])


Solonaru Maria

ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.6 0.3 0.4]) h21=figure(2) set(h21,'color',[0.9 0.7 0.5]) set(h21,'name','Masterand Maria Solonaru, RCSC, an I') h22=plot(timp,estvest,[0 timp(end)],[0,0]) set(h22(1),'color',[0.7 0.5 0.1]) set(h22(1),'linewidth',[0.5]) set(h22(2),'color',[0.5 0.4 0.5]) set(h22(2),'linewidth',[0.5]) set(h22(2),'linestyle','--') h23=title('Seism Time, est-vest'); set(h23,'fontname','times','fontsize',18) set(h23,'color',[0.6 0.5 0.3]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.4 0.3 1]) h31=figure(3) set(h31,'color',[0.4 0.7 0.6]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(timp,vertical,[0 timp(end)],[0,0]) set(h32(1),'color',[0.1 0.8 0.7]) set(h32(1),'linewidth',[0.5]) set(h32(2),'color',[0.5 0.2 0.3]) set(h32(2),'linewidth',[1]) set(h32(2),'linestyle','--') h33=title('Seism Time, vertical'); set(h33,'fontname','times','fontsize',18) set(h33,'color',[1 0 0]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.9 0.1 0.3]) h41=figure(4) set(h41,'color',[0.6 0.7 0.2]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') subplot(3,1,1) plot(timp,nordsud) subplot(3,1,2) plot(timp,estvest) subplot(3,1,3) plot(timp,vertical)

3. Rezultate


Solonaru Maria

Seism 5 : Near E. Coast of Honshu, Japan, 16 mai 1968


Să se traseze graficele înregistrării seismului de pe Coasta de Est a Insulei Honshu din

Japonia, 16 mai 1968, pentru componentele nord-sud, est-vest şi vertical, pentru pasul de

timp 0.02.



% Masterand Solonaru Maria, RCSC, an I clear all close all disp('Grafic cutremur Near E. Coast of Honshu, Japan ') load NEAR.ACC [n,m]=size(NEAR);


Solonaru Maria

timp=0:0.02:(n-1)*0.02; nordsud=NEAR(:,2); [y1max,i1max]=max(nordsud); [y1min,i1min]=min(nordsud); estvest=NEAR(:,1); vertical=NEAR(:,3); h11=figure(1) set(h11,'color',[0.8 0.3 0.3]) set(h11,'name','Masterand Maria Solonaru, RCSC, an I') h12=plot(timp,nordsud,[0 timp(end)],[0,0]) set(h12(1),'color',[0.1 0.8 0.5]) set(h12(1),'linewidth',[0.5]) set(h12(2),'color',[1 0.3 0.8]) set(h12(2),'linewidth',[0.5]) set(h12(2),'linestyle','--') h13=title('Seism Near E. Coast of Honshu, Japan, nord-sud'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0.1 0.2 0.3]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.6 0.8 1]) h21=figure(2) set(h21,'color',[0.3 0.7 0.2]) set(h21,'name','Masterand Maria Solonaru, RCSC, an I') h22=plot(timp,estvest,[0 timp(end)],[0,0]) set(h22(1),'color',[1 0.5 0.5]) set(h22(1),'linewidth',[0.5]) set(h22(2),'color',[0.5 0 0.5]) set(h22(2),'linewidth',[0.5]) set(h22(2),'linestyle','--') h23=title('Seism Near E. Coast of Honshu, Japan, est-vest'); set(h23,'fontname','times','fontsize',18) set(h23,'color',[0 0.5 0.3]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.4 0.3 0.45]) h31=figure(3) set(h31,'color',[0.4 0 0.9]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(timp,vertical,[0 timp(end)],[0,0]) set(h32(1),'color',[0.1 0.75 0.7]) set(h32(1),'linewidth',[0.5]) set(h32(2),'color',[0.5 0.25 0.3]) set(h32(2),'linewidth',[1]) set(h32(2),'linestyle','--') h33=title('Seism Near E. Coast of Honshu, Japan, vertical'); set(h33,'fontname','times','fontsize',18) set(h33,'color',[0 0 0]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.95 0.1 0.75])


Solonaru Maria

h41=figure(4) set(h41,'color',[0.6 0.25 0.2]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') subplot(3,1,1) plot(timp,nordsud) subplot(3,1,2) plot(timp,estvest) subplot(3,1,3) plot(timp,vertical)

3. Rezultate

Seism 6 : Lytle Creek, 12 septembrie 1970


Să se traseze graficele înregistrării seismului din Kobe, 12 septembrie 1970, pentru



Solonaru Maria



% Masterand Solonaru Maria, RCSC, an I clear all close all disp('Grafic cutremur Lytle Creek ') load LYTLE.ACC [n,m]=size(LYTLE); timp=0:0.02:(n-1)*0.02; nordsud=LYTLE(:,2); [y1max,i1max]=max(nordsud); [y1min,i1min]=min(nordsud); estvest=LYTLE(:,1); vertical=LYTLE(:,3); h11=figure(1) set(h11,'color',[0.8 0.8 0.8]) set(h11,'name','Masterand Maria Solonaru, RCSC, an I') h12=plot(timp,nordsud,[0 timp(end)],[0,0]) set(h12(1),'color',[0.2 0.2 0.2]) set(h12(1),'linewidth',[0.5]) set(h12(2),'color',[1 1 0.5]) set(h12(2),'linewidth',[0.5]) set(h12(2),'linestyle','--') h13=title('Seism Lytle Creek, nord-sud'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0.7 0.6 0.3]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.6 0.4 1]) h21=figure(2) set(h21,'color',[0.3 1 1]) set(h21,'name','Masterand Maria Solonaru, RCSC, an I') h22=plot(timp,estvest,[0 timp(end)],[0,0]) set(h22(1),'color',[1 0.3 0.6]) set(h22(1),'linewidth',[0.5]) set(h22(2),'color',[0.5 0.2 0.5]) set(h22(2),'linewidth',[0.5]) set(h22(2),'linestyle','--') h23=title('Seism Lytle Creek, est-vest'); set(h23,'fontname','times','fontsize',18) set(h23,'color',[1 0.8 0.3]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.4 0.3 0.45]) h31=figure(3) set(h31,'color',[0.4 1 0.4]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(timp,vertical,[0 timp(end)],[0,0]) set(h32(1),'color',[0.7 0.7 0.7]) set(h32(1),'linewidth',[0.5])


Solonaru Maria

set(h32(2),'color',[0.9 0.6 0.8]) set(h32(2),'linewidth',[1]) set(h32(2),'linestyle','--') h33=title('Seism Lytle Creek, vertical'); set(h33,'fontname','times','fontsize',18) set(h33,'color',[0.9 0.3 0.1]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.95 0.1 0.75]) h41=figure(4) set(h41,'color',[0.7 0.5 0.1]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') subplot(3,1,1) plot(timp,nordsud) subplot(3,1,2) plot(timp,estvest) subplot(3,1,3) plot(timp,vertical)

3. Rezultate


Solonaru Maria

PROBLEMA NR. 3 - IMPULS

Structuri cu 1GDL – răspuns liber neamortizat la impuls – varianta 1


Să se traseze grafice privind răspunsul liber neamortizat al structurilor cu un grad de libertate

dinamică pentru deplasări, viteze, acceleraţii, forţă tăietoare, moment încovoietor, efort unitar

normal, efort unitar tangenţial şi un grafic comparativ al primelor trei.


Date de intrare:

1 , 1

1 ∙ ℎ


Solonaru Maria

bs – lăţimea secţiunii;

hs – înălţimea secţiunii;

m – masa structurii;

E – modulul de elasticitate longitudinal al materialului;

h – înălţimea grinzii;

În cadrul programului efectuat se vor calcula caracteristici geometrice şi dinamice ale

structurii cu un grad de libertate dinamic.

I – momentul de inerţie al secţiunii

𝐼 =𝑏𝑠 ∙ ℎ 𝑠

3

12 𝑚4

𝛿 – flexibilitatea

𝛿 =1

𝐸𝐼∙ℎ∙ ℎ2

2

2

3=

ℎ3

3𝐸𝐼

k – rigiditatea

𝑘 = 1/𝛿

ω – pulsaţia

𝜔 = 𝑘

𝑚

T – perioada proprie de vibraţie

𝑇 =2𝜋

𝜔

f – frecvenţa

𝑓 =1

𝑇

În cazul vibraţiilor libere neamortizate se foloseşte ecuaţia diferenţială:

𝑚𝑧 𝑡 + 𝑘𝑧 𝑡 = 0

care poate fi scrisă astfel:

𝑧 𝑡 + 𝜔2𝑧 𝑡 = 0

Condiţii iniţiale: 𝑧 0 = 𝑧0 , 𝑧 0 = 𝑧0

Soluţiile ecuaţiei diferenţiale:

𝑧 𝑡 = 𝑧0 ∙ 𝑐𝑜𝑠 𝜔𝑡 +𝑧0

𝜔sin(𝜔𝑡)


Solonaru Maria

z(t) – reprezintă deplasarea la momentul t

𝑧 𝑡 = −𝜔𝑧0 ∙ 𝑠𝑖𝑛 𝜔𝑡 + 𝑧0 cos(𝜔𝑡)

𝑧 𝑡 - reprezintă viteza la momentul t

𝑧 𝑡 = −𝜔2𝑧0 ∙ 𝑐𝑜𝑠 𝜔𝑡 − 𝜔𝑧0 sin 𝜔𝑡 = −𝜔2𝑧(𝑡)

𝑧 𝑡 – reprezintă acceleraţia la mometul t

În calculul forţei tăietoare, momentului încovoietor, efortului normal şi efortului tangenţial s-

au folosit următoarele formule:

𝑉 = 𝑚 ∙ 𝑧 (t)

𝑀 = 𝑉 ∙ ℎ

𝜎 =𝑀

𝐼·ℎ𝑠

2

𝜏 =𝑉 ℎ𝑠4∙𝐴2

𝐼 ∙ 𝑏𝑠


%Masterand Solonaru Maria, RCSC, an I close all clear all disp('Structuri cu 1 GDL - raspuns liber neamortizat la impuls') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii(cm)='); bs=bs/100; hs=input('inaltimea sectiunii(cm)='); hs=hs/100; m=input('masa structurii(kg)='); E=input('modulul de elasticitate(daN/cm^2)='); E=E*1e5; h=input('inaltimea grinzii(m)=') else bs=20; %latimea sectiunii(cm) bs=bs/100; hs=40; %inaltimea sectiunii(cm) hs=hs/100; m=1e5; %masa structurii(kg) E=2.1e6; %modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii(m) end %calculul caracteristicilor geometrice I=bs*hs^3/12; % momentul sectional de inertie(m^4)


Solonaru Maria

% calculul caracteristicilor elastice delta=h^3/3/E/I; % flexibilitatea (m/N) k=1/delta; %rigiditatea (N/m) % calculul caracteristicilor dinamice omega =sqrt(k/m); %pulsatia (frecventa circulara)(rad/s) T=2*pi/omega; % perioada proprie de vibratie(s) f=1/T; % frecventa proprie(Hz) %conditii initiale zp0=200; %viteza initiala (cm/s) zp0=zp0/100; % (m/s) z0=0 % se considera deplasarea initiala nula t=0:0.01:5; % intervalul de timp al raspunsului (s) z=((zp0*sin(omega*t))/omega+z0*cos(omega*t)); %raspunsul in deplasari (m) h11=figure(1); set(h11,'color',[0.8 1 0.3]) set(h11,'name','Masterand Maria Solonaru, RCSC, an I') h12=plot(t,z,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h12(1),'color',[1 0.6 0.4]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.5 0.3 0.7]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('Raspunsul liber neamortizat la impuls - deplasari'); set(h13,'fontname','times','fontsize',16') set(h13,'color',[0.3 0.6 1]) h14=xlabel('timp (s)'); set(h14,'fontname','times','fontsize',20) set(h14,'color',[ 0.2 0.7 0.5]) h15=ylabel('deplasare (m)'); set(h15,'fontname','times','fontsize',18) set(h15,'color',[ 0.9 0.5 0.6]) set(gca,'color',[0.8 0.5 0.6]) %calculul minimului si maximului [zmax,imax]=max(z); [zmin,imin]=min(z); h16=text(t(imax)*1.10,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(z(imax))]) set(h16,'fontweight','bold') h17=text(t(imin)*1.10,0.95*zmin,['minim=',num2str(zmin),' pentru t=',num2str(z(imin))]) set(h17,'fontweight','bold') zp=(zp0*cos(omega*t)-omega*z0*sin(omega*t)); %raspunsul in viteze (m) h21=figure(2) plot(t,zp) set(h21,'color',[0.8 0.3 0.3]) set(h21,'name','Masterand Maria Solonaru, RCSC, an I') h22=plot(t,zp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h22(1),'color',[0.4 0.5 0]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.5 0.6 0.4]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspunsul liber neamortizat la impuls - viteze'); set(h23,'fontname','times','fontsize',16') set(h23,'color',[ 0.6 0.9 0.7]) h24=xlabel('timpul (t)'); set(h24,'fontname','times','fontsize',20) set(h24,'color',[ 0.4 0.9 0.5]) h25=ylabel('viteza m/s'); set(h25,'fontname','times','fontsize',18) set(h25,'color',[ 0.5 0.3 0.9]) set(gca,'color',[0.4 0.4 0.4])


Solonaru Maria

%calculul minimului si maximului [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h26=text(t(imax)*1.10,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(zp(imax))]) set(h26,'fontweight','bold') h27=text(t(imin)*1.10,0.95*zpmin,['minim=',num2str(zpmin),' pentru t=',num2str(zp(imin))]) set(h27,'fontweight','bold') zpp=-((omega^2)*z); %raspunsul in acceleratii(m/s^2) h31=figure(3) plot(t,zpp) set(h31,'color',[0.9 0.1 0.6]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(t,zpp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h32(1),'color',[0.1 1 0.8]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.8 0.3 0.4]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspunsul liber neamortizat la impuls - acceleratii'); set(h33,'fontname','times','fontsize',16') set(h33,'color',[ 0.9 0.6 0.4]) h34=xlabel('timpul (t)'); set(h34,'fontname','times','fontsize',20) set(h34,'color',[ 0.8 0.7 0.1]) h35=ylabel('acceleratia m/s^2'); set(h35,'fontname','times','fontsize',18) set(h35,'color',[ 0.9 0.1 0.1]) set(gca,'color',[0.4 0.5 0.6]) %calculul minimului si maximului [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h36=text(t(imax)*1.10,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(zpp(imax))]) set(h36,'fontweight','bold') h37=text(t(imin)*1.10,0.95*zppmin,['minim=',num2str(zppmin),' pentru t=',num2str(zpp(imin))]) set(h37,'fontweight','bold') h41=figure(4) %grafic comparativ set(h41,'color',[1 0.1 0.1]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') subplot(3,1,1) plot(t,z) subplot(3,1,2) plot(t,zp) subplot(3,1,3) plot(t,zpp) V=m*zpp h51=figure(5) %Graficul fortei taietoare plot(t,V); set(h51,'color',[0.4 0.6 0.4]); set(h51,'name','Masterand Maria Solonaru, RCSC, an I'); h52=plot(t,V,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h52(1),'color',[0.5 0.9 0.1]); set(h52(1),'linewidth',[2]); set(h52(2),'color',[0.8 1 0.4]); set(h52(2),'linewidth',[2]); set(h52(2),'linestyle','--'); h53=title('Graficul fortei taietoare'); set(h53,'fontname','times','fontsize',16') set(h53,'color',[ 0.6 0.2 0.1]); h54=xlabel('timpul (t)'); set(h54,'fontname','times','fontsize',20)


Solonaru Maria

set(h54,'color',[ 0.1 0.9 0.1]); h55=ylabel('ft'); set(h55,'fontname','times','fontsize',18) set(h55,'color',[ 0.1 0.9 0.1]); set(gca,'color',[0.4 0.2 0.3]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h56=text(t(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(V(imax))]) set(h56,'fontweight','bold') h57=text(t(imin)*1.10,0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(V(imin))]) set(h57,'fontweight','bold') M=V*h h61=figure(6) %Graficul momentului incovoietor plot(t,M); set(h61,'color',[0.1 0.5 0.2]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(t,M,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h62(1),'color',[0 0.7 0.1]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.3 1 0.1]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul momentului incovoietor'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.3 0.9 0.3]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.9 0.3 0.1]); h65=ylabel('mi'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.5 0.1 0.5]); set(gca,'color',[0.4 0.3 0.6]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h66=text(t(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(M(imax))]) set(h66,'fontweight','bold') h67=text(t(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(M(imin))]) set(h67,'fontweight','bold') sigma =(M*hs)/(2*I) h71=figure(7) %Graficul efortului axial plot(t,sigma); set(h71,'color',[0.3 0.4 0.7]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(t,sigma,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h72(1),'color',[0.8 0.1 0.4]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.3 0.5 0.9]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul efortului axial'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.3 0.9 0.6]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.7 0.5 0.2]); h75=ylabel('sigma'); set(h75,'fontname','times','fontsize',18) set(h75,'color',[ 0.1 1 0.2]);


Solonaru Maria

set(gca,'color',[0.4 0.3 0.4]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h76=text(t(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(sigma(imax))]) set(h76,'fontweight','bold') h77=text(t(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(sigma(imin))]) set(h77,'fontweight','bold') tau =(V*hs^2)/(8*I) h81=figure(8) %Graficul efortului tangential plot(t,tau); set(h81,'color',[0.6 0 0.2]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(t,tau,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h82(1),'color',[0.3 0.6 0]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.3 0.4 0.8]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului tangential'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.4 0.7 0.1]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.8 0.7 0.5]); h85=ylabel('tau'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.2 0.9 0.3]); set(gca,'color',[0.7 0.8 0.1]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h86=text(t(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(tau(imax))]) set(h86,'fontweight','bold') h87=text(t(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(tau(imin))]) set(h87,'fontweight','bold

4. Rezultate


Solonaru Maria

Structuri cu 1GDL – răspuns liber amortizat la impuls – varianta 1



Solonaru Maria

Să se traseze grafice privind răspunsul liber amortizat al structurilor cu un grad de libertate




Date de intrare:










3

12 𝑚4


𝛿 =1


2

2

3=

ℎ3

3𝐸𝐼

k – rigiditatea

𝑘 = 1/𝛿

ω – pulsaţia

1 , 1

1 ∙ ℎ


Solonaru Maria

𝜔 = 𝑘

𝑚


𝑇 =2𝜋

𝜔

f – frecvenţa

𝑓 =1

𝑇

În cazul vibraţiilor libere amortizate se foloseşte ecuaţia diferenţială:

𝑚𝑧 𝑡 + 𝑐𝑧 𝑡 + 𝑘𝑧 𝑡 = 0


𝑧 𝑡 + 2𝜈𝜔𝑧 𝑡 + 𝜔2𝑧 𝑡 = 0



𝑧 𝑡 = 𝑧0 ∙ 𝑐𝑜𝑠 𝜔 𝑡 +𝑧0 + 𝜈𝜔𝑧0

𝜔sin(𝜔 𝑡) 𝑒−𝜈𝜔𝑡


𝑧 𝑡 = −𝜔 𝑧0 ∙ 𝑠𝑖𝑛 𝜔 𝑡 + 𝜔 𝑧0 + 𝜈𝜔𝑧0

𝜔cos(𝜔 𝑡) 𝑒−𝜈𝜔𝑡

− 𝜈𝜔 𝑧0 ∙ 𝑐𝑜𝑠 𝜔 𝑡 +𝑧0 + 𝜈𝜔𝑧0



𝑧 𝑡 = −𝜔 2𝑧0 ∙ 𝑐𝑜𝑠 𝜔 𝑡 − 𝜔 2𝑧0 + 𝜈𝜔𝑧0


− 𝜈𝜔 𝑧0 ∙ 𝑐𝑜𝑠 𝜔 𝑡 + 𝜔 𝑧0 + 𝜈𝜔𝑧0


− 𝜈𝜔 −𝜔 𝑧0 ∙ 𝑠𝑖𝑛 𝜔 𝑡 + 𝜔 𝑧0 + 𝜈𝜔𝑧0


+ 𝜈2𝜔2 𝑧0 ∙ 𝑐𝑜𝑠 𝜔 𝑡 +𝑧0 + 𝜈𝜔𝑧0

𝜔sin(𝜔 𝑡) 𝑒−𝜈𝜔𝑡 = −𝜔2𝑧 𝑡 − 2𝜈𝜔𝑧

𝜔 = 𝜔 1 − 𝜈2 (pseudopulsaţia)



Solonaru Maria



𝑉 = 𝑚 ∙ 𝑧 (t)

𝑀 = 𝑉 ∙ ℎ

𝜎 =𝑀

𝐼·ℎ𝑠

2


𝐼 ∙ 𝑏𝑠


%Masterand Maria Solonaru, RCSC, an I close all clear all disp('Structuri cu 1 GDL - raspuns liber amortizat la impuls - varianta 1') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii(cm)='); bs=bs/100; hs=input('inaltimea sectiunii(cm)='); hs=hs/100; m=input('masa structurii (kg)='); E=input('modulul de elasticitate (daN/cm^2)='); E=E*1e5; niu=input('procentul din amortizarea critica(%)='); niu=niu/100; h=input('inaltimea grinzii(m)=') else bs=20; %latimea sectiunii(cm) bs=bs/100; hs=40; %inaltimea sectiunii(cm) hs=hs/100; m=1e5; %masa structurii(kg) E=2.1e6; %modulul de elasticitate(daN/cm^2) E=E*1e5; niu=5; %procentul din amortizarea critica(%) niu=niu/100; h=4; %inaltimea grinzii(m) end %calculul caracteristicilor geometrice I=bs*hs^3/12; % momentul sectional de inertie(m^4) % calculul caracteristicilor elastice delta=h^3/3/E/I; % flexibilitatea (m/N) k=1/delta; %rigiditatea (N/m) % calculul caracteristicilor dinamice omega =sqrt(k/m); %pulsatia (frecventa circulara)(rad/s) T=2*pi/omega; % perioada proprie de vibratie(s) f=1/T; % frecventa proprie(Hz) omegab=omega*sqrt(1-niu^2); %pulsatia (frecventa circulara)in regim amortizat(rad/s) Tb=T/sqrt(1-niu^2);% perioada proprie de vibratie in regim amortizat(s)


Solonaru Maria

fb=f*sqrt(1-niu^2); %frecventa in regim liber amortizat %raspunsul liber amortizat la impuls al structurii cu 1 gdl %conditii initiale %se considera deplasarea initiala nula, z0=0 zp0=200; %viteza initiala (cm/s) zp0=zp0/100; % (m/s) %raspunsul liber amortizat t=0:0.01:5; % intervalul de timp al raspunsului(s) z=(zp0/omegab*sin(omegab*t)).*exp(-niu*omega*t); %raspunsul in deplasari (m) inf=zp0/omegab*exp(-niu*omega*t); h11=figure(1); set(h11,'color',[0.1 0.4 0.3]) set(h11,'name','Masterand Maria Solonaru, RCSC, an I') h12=plot(t,z,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h12(1),'color',[0 1 1]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.8 0.2 0.7]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('Raspunsul liber amortizat la impuls - deplasari'); set(h13,'fontname','times','fontsize',16') set(h13,'color',[ 0.3 0.8 0.4]) h14=xlabel('timp (s)'); set(h14,'fontname','times','fontsize',20) set(h14,'color',[ 0.7 0.5 0.5]) h15=ylabel('deplasare'); set(h15,'fontname','times','fontsize',18) set(h15,'color',[ 0.4 0.2 0.1]) set(gca,'color',[0.4 0.5 0.7]) %calculul minimului si maximului [zmax,imax]=max(z); [zmin,imin]=min(z); h16=text(t(imax)*1.10,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(z(imax))]) set(h16,'fontweight','bold') h17=text(t(imin)*1.10,0.95*zmin,['minim=',num2str(zmin),' pentru t=',num2str(z(imin))]) set(h17,'fontweight','bold') zp=zp0*cos(omegab*t).*exp(-niu*omega*t)-niu*omega*z; %raspunsul in viteze (m) h21=figure(2) plot(t,zp) set(h21,'color',[0.2 0.8 0.9]) set(h21,'name','Masterand Maria Solonaru, RCSC, an I') h22=plot(t,zp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h22(1),'color',[0.4 0.9 0.1]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.7 0.2 0.2]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspunsul liber amortizat la impuls - viteze'); set(h23,'fontname','times','fontsize',16') set(h23,'color',[ 0.8 0.7 0.1]) h24=xlabel('timpul (t)'); set(h24,'fontname','times','fontsize',20) set(h24,'color',[1 0.1 0.8]) h25=ylabel('viteza m/s'); set(h25,'fontname','times','fontsize',18) set(h25,'color',[ 0 0 0.1]) set(gca,'color',[0.9 0.6 0.6]) %calculul minimului si maximului [zpmax,imax]=max(zp); [zpmin,imin]=min(zp);


Solonaru Maria

h26=text(t(imax)*1.10,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(zp(imax))]) set(h26,'fontweight','bold') h27=text(t(imin)*1.10,0.95*zpmin,['minim=',num2str(zpmin),' pentru t=',num2str(zp(imin))]) set(h27,'fontweight','bold') zpp=-2*niu*omega*zp-(omega^2)*z; %raspunsul in acceleratii(m/s^2) h31=figure(3) plot(t,zpp) set(h31,'color',[0.9 0 0.3]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(t,zpp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h32(1),'color',[0 0.6 1]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.2 0.7 0.4]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspunsul liber amortizat la impuls - acceleratii'); set(h33,'fontname','times','fontsize',16') set(h33,'color',[ 0.6 0.9 0.7]) h34=xlabel('timpul (t)'); set(h34,'fontname','times','fontsize',20) set(h34,'color',[ 0.4 0.9 0.5]) h35=ylabel('acceleratia m/s^2'); set(h35,'fontname','times','fontsize',18) set(h35,'color',[ 0.1 0.5 0.1]) set(gca,'color',[0.4 0 0.6]) %calculul minimului si maximului [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h36=text(t(imax)*1.10,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(zpp(imax))]) set(h36,'fontweight','bold') h37=text(t(imin)*1.10,0.95*zppmin,['minim=',num2str(zppmin),' pentru t=',num2str(zpp(imin))]) set(h37,'fontweight','bold') h41=figure(4) %grafic comparativ set(h41,'color',[0.2 0.1 0.3]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') subplot(3,1,1) plot(t,z) subplot(3,1,2) plot(t,zp) subplot(3,1,3) plot(t,zpp) V=m*zpp h51=figure(5) %Graficul fortei taietoare plot(t,V); set(h51,'color',[0.7 0.7 0.2]); set(h51,'name','Masterand Maria Solonaru, RCSC, an I'); h52=plot(t,V,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h52(1),'color',[1 1 0]); set(h52(1),'linewidth',[2]); set(h52(2),'color',[0.9 0.4 0.4]); set(h52(2),'linewidth',[2]); set(h52(2),'linestyle','--'); h53=title('Graficul fortei taietoare'); set(h53,'fontname','times','fontsize',16') set(h53,'color',[ 0.4 0.9 0.7]); h54=xlabel('timpul (t)'); set(h54,'fontname','times','fontsize',20) set(h54,'color',[ 0 0.9 0.1]); h55=ylabel('ft'); set(h55,'fontname','times','fontsize',18)


Solonaru Maria

set(h55,'color',[ 0.3 0.7 0.1]); set(gca,'color',[0.9 0.4 0.6]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h56=text(t(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(V(imax))]) set(h56,'fontweight','bold') h57=text(t(imin)*1.10,0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(V(imin))]) set(h57,'fontweight','bold') M=V*h h61=figure(6) %Graficul momentului incovoietor plot(t,M); set(h61,'color',[0.7 0.4 0.3]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(t,M,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h62(1),'color',[0.3 0.9 0.2]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.5 0.1 0.7]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul momentului incovoietor'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.7 0.8 0.3]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.9 0.1 0.5]); h65=ylabel('mi'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.6 0.1 0.5]); set(gca,'color',[0.4 0.1 0.6]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h66=text(t(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(M(imax))]) set(h66,'fontweight','bold') h67=text(t(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(M(imin))]) set(h67,'fontweight','bold') sigma =(M*hs)/(2*I) h71=figure(7) %Graficul efortului axial plot(t,sigma); set(h71,'color',[0.4 0.8 0.3]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(t,sigma,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h72(1),'color',[0.4 0.7 0.7]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.5 0.4 0.4]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul efortului axial'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.6 0.2 0.7]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.7 0.2 0.6]); h75=ylabel('sigma'); set(h75,'fontname','times','fontsize',18) set(h75,'color',[ 0.1 0.8 0.1]); set(gca,'color',[0.4 0.3 0.6]); %calculul minimului si maximului [sigmamax,imax]=max(sigma);


Solonaru Maria

[sigmamin,imin]=min(sigma); h76=text(t(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(sigma(imax))]) set(h76,'fontweight','bold') h77=text(t(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(sigma(imin))]) set(h77,'fontweight','bold') tau =(V*hs^2)/(8*I) h81=figure(8) %Graficul efortului tangential plot(t,tau); set(h81,'color',[0.5 0.5 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(t,tau,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h82(1),'color',[0.3 0.6 0.6]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.5 0.3 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului tangential'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.7 0.4 0.1]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.8 0.6 0.5]); h85=ylabel('tau'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.2 0.9 0.1]); set(gca,'color',[0.4 0.3 0.6]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h86=text(t(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(tau(imax))]) set(h86,'fontweight','bold') h87=text(t(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(tau(imin))]) set(h87,'fontweight','bold')

4. Rezultate


Solonaru Maria



Solonaru Maria

1. Programarea problemei % masterand Maria Solonaru, RCSC, an I close all clear all disp('Structuri cu 1 GDL - raspuns liber neamortizat - varianta 2') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii (cm)='); bs=bs/100; hs=input('inaltimea sectiunii (cm)='); hs=hs/100; m=input('masa (kg)='); E=input('modulul de elasticitate(daN/cm^2)='); E=E*1e5; h=input('inaltimea grinzii (m)='); else bs=20; %latimea sectiunii bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) %calculul caracteristicilor geometrice %momentul de inertie (m^4) I=bs*hs^3/12; end %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamice omega=sqrt(k/m); %pulsatia (rad/s) T=2*pi/omega; %perioada proprie de vibratie(s) f=1/T; % frecventa proprie (Hz) %raspunsul liber neamortizat la impuls al structurii cu 1GDL %conditii initiale H0=2e5; % kg*m/s impuls initial zp0=H0/m;%viteza initiala (m/s) %raspunsul liber neamortizat t=0:0.01:5; %intervalul de timp al raspunsului z0=0; z=((zp0*sin(omega*t))/omega+z0*cos(omega*t));%raspunsul in deplasari h11=figure(1) set(h11,'name','Masterand Solonaru Maria - RCSC an I') set(h11,'color',[0.9 0.1 0.8]) h12=plot(t,z,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h12(1),'color',[0 1 0.5]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.8 0.1 0.4]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('Raspunsul liber neamortizat la impuls - deplasari'); set(h13,'fontname','times','fontsize',16') set(h13,'color',[ 0.2 0.9 0.7]) h14=xlabel('timp (s)'); set(h14,'fontname','times','fontsize',20)


Solonaru Maria

set(h14,'color',[ 0.4 0.2 0.1]) h15=ylabel('deplasare (m)'); set(h15,'fontname','times','fontsize',18) set(h15,'color',[ 0.3 0.4 0.1]) set(gca,'color',[0.9 0.3 0.6]) %calculul minimului si maximului [zmax,imax]=max(z); [zmin,imin]=min(z); h16=text(t(imax)*1.10,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(z(imax))]) set(h16,'fontweight','bold') h17=text(t(imin)*1.10,0.95*zmin,['minim=',num2str(zmin),' pentru t=',num2str(z(imin))]) set(h17,'fontweight','bold') zp=(zp0*cos(omega*t)-omega*z0*sin(omega*t)); %raspunsul in viteze (m) h21=figure(2) plot(t,zp) set(h21,'color',[0.9 0.2 0.7]) set(h21,'name','Masterand Maria Solonaru, RCSC, an I') h22=plot(t,zp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h22(1),'color',[0.5 1 0.3]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.3 0.7 0.7]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspunsul liber neamortizat la impuls - viteze'); set(h23,'fontname','times','fontsize',16') set(h23,'color',[ 0.6 0.2 0.7]) h24=xlabel('timpul (t)'); set(h24,'fontname','times','fontsize',18) set(h24,'color',[ 0.8 0.2 0.5]) h25=ylabel('viteza m/s'); set(h25,'fontname','times','fontsize',18) set(h25,'color',[ 0.7 0.5 0.1]) set(gca,'color',[0.4 0.8 0.6]) %calculul minimului si maximului [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h26=text(t(imax)*1.10,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(zp(imax))]) set(h26,'fontweight','bold') h27=text(t(imin)*1.10,0.95*zpmin,['minim=',num2str(zpmin),' pentru t=',num2str(zp(imin))]) set(h27,'fontweight','bold') zpp=-((omega^2)*z); %raspunsul in acceleratii(m/s^2) h31=figure(3) plot(t,zpp) set(h31,'color',[0.7 0.2 0.8]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(t,zpp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h32(1),'color',[0.6 0.7 0]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.5 0.2 0.4]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspunsul liber neamortizat la impuls - acceleratii'); set(h33,'fontname','times','fontsize',16') set(h33,'color',[ 0.3 0.9 0.7]) h34=xlabel('timpul (t)'); set(h34,'fontname','times','fontsize',20) set(h34,'color',[ 0.8 0.2 0.1]) h35=ylabel('acceleratia m/s^2'); set(h35,'fontname','times','fontsize',18) set(h35,'color',[ 0 0.5 0.1])


Solonaru Maria

set(gca,'color',[0.4 0.2 0.6]) %calculul minimului si maximului [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h36=text(t(imax)*1.10,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(zpp(imax))]) set(h36,'fontweight','bold') h37=text(t(imin)*1.10,0.95*zppmin,['minim=',num2str(zppmin),' pentru t=',num2str(zpp(imin))]) set(h37,'fontweight','bold') h41=figure(4) %grafic comparativ set(h41,'color',[0.8 0.2 0.3]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') subplot(3,1,1) plot(t,z) subplot(3,1,2) plot(t,zp) subplot(3,1,3) plot(t,zpp) V=m*zpp h51=figure(5) %Graficul fortei taietoare plot(t,V); set(h51,'color',[0.7 0.2 0.5]); set(h51,'name','Masterand Maria Solonaru, RCSC, an I'); h52=plot(t,V,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h52(1),'color',[0.5 0.9 0]); set(h52(1),'linewidth',[2]); set(h52(2),'color',[0.5 0 0.4]); set(h52(2),'linewidth',[2]); set(h52(2),'linestyle','--'); h53=title('Graficul fortei taietoare'); set(h53,'fontname','times','fontsize',16') set(h53,'color',[ 0.6 0.8 0.7]); h54=xlabel('timpul (t)'); set(h54,'fontname','times','fontsize',20) set(h54,'color',[ 0.1 0.9 0]); h55=ylabel('ft'); set(h55,'fontname','times','fontsize',18) set(h55,'color',[ 0.4 0.1 0.7]); set(gca,'color',[0.4 0.3 0.6]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h56=text(t(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(V(imax))]) set(h56,'fontweight','bold') h57=text(t(imin)*1.10,0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(V(imin))]) set(h57,'fontweight','bold') M=V*h h61=figure(6) %Graficul momentului incovoietor plot(t,M); set(h61,'color',[0.8 0.3 0.3]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(t,M,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h62(1),'color',[1 0.9 0]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.2 0.1 0.4]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul momentului incovoietor'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.4 0.9 0.3]); h64=xlabel('timpul (t)');


Solonaru Maria

set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.8 0.9 0.1]); h65=ylabel('mi'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.1 0.6 0.4]); set(gca,'color',[0.4 0.5 0.6]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h66=text(t(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(M(imax))]) set(h66,'fontweight','bold') h67=text(t(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(M(imin))]) set(h67,'fontweight','bold') sigma =(M*hs)/(2*I) h71=figure(7) %Graficul efortului axial plot(t,sigma); set(h71,'color',[0.9 0.7 0.3]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(t,sigma,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h72(1),'color',[0.1 1 0.7]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.5 0.3 0.4]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul efortului axial'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.6 0.5 0.7]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.9 0.4 0.1]); h75=ylabel('sigma'); set(h75,'fontname','times','fontsize',18) set(h75,'color',[ 0.3 0.9 0.1]); set(gca,'color',[0.4 0.2 0.6]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h76=text(t(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(sigma(imax))]) set(h76,'fontweight','bold') h77=text(t(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(sigma(imin))]) set(h77,'fontweight','bold') tau =(V*hs^2)/(8*I) h81=figure(8) %Graficul efortului tangential plot(t,tau); set(h81,'color',[0.9 0.2 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(t,tau,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h82(1),'color',[0.4 0.6 0.8]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.5 0.3 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului tangential'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.1 0.9 0]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.8 0.2 0.5]); h85=ylabel('tau');


Solonaru Maria

set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.4 0.8 0.1]); set(gca,'color',[0.7 0.6 0.9]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h86=text(t(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(tau(imax))]) set(h86,'fontweight','bold') h87=text(t(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(tau(imin))]) set(h87,'fontweight','bold')

2. Rezultate


Solonaru Maria


1. Programarea problemei % masterand Maria Solonaru close all clear all disp('Structuri cu 1GDL - raspuns liber amortizat - varianta 2') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii (cm)='); bs=bs/100; hs=input('inaltimea sectiunii (cm)='); hs=hs/100; m=input('masa (kg)='); niu=input('procentul din amortizarea critica (%)='); niu=niu/100; E=input('modulul de elasticitate(daN/cm^2)=');


Solonaru Maria

E=E*1e5; h=input('inaltimea grinzii (m)='); else bs=20; %latimea sectiunii bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) niu=5; %procentul din amortizarea critica (%) niu=niu/100; E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) end %calculul caracteristicilor geometrice %momentul de inertie (m^4) I=bs*hs^3/12; %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamice omega=sqrt(k/m); %pulsatia (rad/s) T=2*pi/omega; %perioada proprie de vibratia(s) f=1/T; % frecventa proprie (Hz) omegab=omega*sqrt(1-niu^2); %pulsatia in regim liber amortizat Tb=T/sqrt(1-niu^2); % perioada de vibratie in regim liber amortizat fb=1/Tb; %raspunsul liber amortizat la impuls al structurii cu 1GDL %conditii initiale H0=2e5; % kg*m/s impuls initial zp0=H0/m;%viteza initiala (m/s) %raspunsul liber amortizat t=0:0.1:5; %intervalul de timp al raspunsului z=(zp0/omegab*sin(omegab*t)).*exp(-niu*omega*t); %raspunsul in deplasari inf=zp0/omegab*exp(-niu*omega*t); h11=figure(1) set(h11,'name','masterand Solonaru Maria - RCSC an I') set(h11,'color',[0.5 0.3 0.2]) h12=plot(t,z,[0 t(end)],[0 0],'--',inf,-inf) set(gca,'color',[0.5 0.1 0.8]) set(h12(1),'color',[0.3 1 0.8]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.8 0.2 0.5]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('Raspuns liber amortizat la impuls deplasare'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0.4 0.5 1]) h14=xlabel('timpul (s)'); set(h14,'fontname','times','fontsize',16) set(h14,'color',[0.8 0 0.6]) h15=ylabel('deplasarea (m)'); set(h15,'fontname','times','fontsize',16) set(h15,'color',[0.3 0.6 0.8]) set(gca,'color',[0.9 0.3 0.2]) %calc max si min [zmax,imax]=max(z); [zmin,imin]=min(z);


Solonaru Maria

h16=text(t(imax)*1.10,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(t(imax))]) set(h16,'fontweight','bold') h17=text(t(imin)*1.10,0.95*zmin,['minim=',num2str(zmin),'pentru t=',num2str(t(imin))]) set(h17,'fontweight','bold') set(h11,'Position',[150 50 600 500]) zp=zp0*cos(omegab*t).*exp(-niu*omega*t)-niu*omega*z; %raspunsul in viteze h21=figure(2) plot(t,zp) set(h21,'color',[0.1 0.9 0.3]) set(h21,'name','Masterand Maria Solonaru, RCSC, an I') h22=plot(t,zp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h22(1),'color',[0.1 0.7 0.9]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[1 1 0.4]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspunsul liber amortizat la impuls - viteze'); set(h23,'fontname','times','fontsize',16') set(h23,'color',[ 0.9 0.2 0.1]) h24=xlabel('timpul (t)'); set(h24,'fontname','times','fontsize',20) set(h24,'color',[ 0.4 0.7 0.5]) h25=ylabel('viteza m/s'); set(h25,'fontname','times','fontsize',18) set(h25,'color',[ 0.2 0.5 0.6]) set(gca,'color',[0.9 0.5 0.6]) %calculul minimului si maximului [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h26=text(t(imax)*1.10,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(zp(imax))]) set(h26,'fontweight','bold') h27=text(t(imin)*1.10,0.95*zpmin,['minim=',num2str(zpmin),' pentru t=',num2str(zp(imin))]) set(h27,'fontweight','bold') zpp=-2*niu*omega*zp-(omega^2)*z; %raspunsul in accelaratii h31=figure(3) plot(t,zpp) set(h31,'color',[0.5 0.9 0.3]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(t,zpp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h32(1),'color',[0.5 0.7 0.7]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.8 0.1 0.7]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspunsul liber amortizat la impuls - acceleratii'); set(h33,'fontname','times','fontsize',16') set(h33,'color',[ 0.2 0.5 0.2]) h34=xlabel('timpul (t)'); set(h34,'fontname','times','fontsize',20) set(h34,'color',[ 0.3 0.7 0.5]) h35=ylabel('acceleratia m/s^2'); set(h35,'fontname','times','fontsize',18) set(h35,'color',[ 0.7 0.5 0.1]) set(gca,'color',[0.9 0.5 0.6]) %calculul minimului si maximului [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h36=text(t(imax)*1.10,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(zpp(imax))]) set(h36,'fontweight','bold') h37=text(t(imin)*1.10,0.95*zppmin,['minim=',num2str(zppmin),' pentru t=',num2str(zpp(imin))])


Solonaru Maria

set(h37,'fontweight','bold') h41=figure(4) %grafic comparativ set(h41,'color',[0.9 0.9 0.3]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') subplot(3,1,1) plot(t,z) subplot(3,1,2) plot(t,zp) subplot(3,1,3) plot(t,zpp) V=m*zpp h51=figure(5) %Graficul fortei taietoare plot(t,V); set(h51,'color',[0.9 0.2 0.3]); set(h51,'name','Masterand Maria Solonaru, RCSC, an I'); h52=plot(t,V,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h52(1),'color',[0.4 0.9 0.9]); set(h52(1),'linewidth',[2]); set(h52(2),'color',[0.5 0.6 0.2]); set(h52(2),'linewidth',[2]); set(h52(2),'linestyle','--'); h53=title('Graficul fortei taietoare'); set(h53,'fontname','times','fontsize',16') set(h53,'color',[ 0.9 0.6 0.7]); h54=xlabel('timpul (t)'); set(h54,'fontname','times','fontsize',20) set(h54,'color',[ 0.7 0.1 0.4]); h55=ylabel('ft'); set(h55,'fontname','times','fontsize',18) set(h55,'color',[ 0.2 0.7 0.1]); set(gca,'color',[0.4 0.3 0.2]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h56=text(t(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(V(imax))]) set(h56,'fontweight','bold') h57=text(t(imin)*1.10,0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(V(imin))]) set(h57,'fontweight','bold') M=V*h h61=figure(6) %Graficul momentului incovoietor plot(t,M); set(h61,'color',[0.9 0.3 0.3]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(t,M,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h62(1),'color',[0.4 0.6 0]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.7 1 0.4]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul momentului incovoietor'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.1 0.6 0.3]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.9 0.4 0.9]); h65=ylabel('mi'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.5 0.9 0.1]); set(gca,'color',[0.4 0.8 0.6]); %calculul minimului si maximului


Solonaru Maria

[Mmax,imax]=max(M); [Mmin,imin]=min(M); h66=text(t(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(M(imax))]) set(h66,'fontweight','bold') h67=text(t(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(M(imin))]) set(h67,'fontweight','bold') sigma =(M*hs)/(2*I) h71=figure(7) %Graficul efortului axial plot(t,sigma); set(h71,'color',[0.3 0.7 0.3]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(t,sigma,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h72(1),'color',[0.3 0.5 0]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.4 1 0.4]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul efortului axial'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.9 0.2 0.7]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.8 0.8 0.1]); h75=ylabel('sigma'); set(h75,'fontname','times','fontsize',18) set(h75,'color',[ 1 0.5 0.1]); set(gca,'color',[0.1 0 0.6]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h76=text(t(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(sigma(imax))]) set(h76,'fontweight','bold') h77=text(t(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(sigma(imin))]) set(h77,'fontweight','bold') tau =(V*hs^2)/(8*I) h81=figure(8) %Graficul efortului tangential plot(t,tau); set(h81,'color',[0.9 0.1 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(t,tau,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h82(1),'color',[1 0.3 1]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.2 0 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului tangential'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.5 0.8 0.1]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 1 0.2 0.9]); h85=ylabel('tau'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.3 0.4 0.1]); set(gca,'color',[0.9 0.1 0]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h86=text(t(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(tau(imax))])


Solonaru Maria

set(h86,'fontweight','bold') h87=text(t(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(tau(imin))]) set(h87,'fontweight','bold')

2. Rezultate


Solonaru Maria


1. Programarea problemei % masterand Maria Solonaru close all clear all disp('Structuri cu 1GDL - Raspuns liber neamortizat la impuls - varianta 3') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii (cm)='); bs=bs/100; hs=input('inaltimea sectiunii (cm)='); hs=hs/100; m=input('masa (kg)='); E=input('modulul de elasticitate(daN/cm^2)='); E=E*1e5; h=input('inaltimea grinzii (m)='); else bs=20; %latimea sectiunii bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) end %calculul caracteristicilor geometrice %momentul de inertie (m^4) I=bs*hs^3/12; %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamice omega=sqrt(k/m); %pulsatia (rad/s)


Solonaru Maria

T=2*pi/omega; %perioada proprie de vibratia(s) f=1/T; % frecventa proprie (Hz) %raspunsul liber neamortizat la impuls seismic al structurii cu 1GDL %conditii initiale upp=10; % acceleratie seismica instantanee m/s^2 pt=0.01;% pasul de timp H0=upp*m*pt; % kg*m/s impuls initial zp0=H0/m;% viteza initiala (m/s) %raspunsul liber neamortizat t=0:0.01:5; %intervalul de timp al raspunsului z0=0; z=((zp0*sin(omega*t))/omega+z0*cos(omega*t)); %raspunsul in deplasari h11=figure(1) set(h11,'name','masterand Solonaru Maria, RCSC, an I') set(h11,'color',[0.1 0.5 0.2]) h12=plot(t,z,[0 t(end)],[0 0],'--',inf,-inf) set(gca,'color',[0.9 0.3 0.5]) set(h12(1),'color',[0.8 0.2 0.6]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.8 0.2 0.5]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('Raspuns liber neamortizat la impuls - deplasari'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[1 0.5 1]) h14=xlabel('timpul (s)'); set(h14,'fontname','times','fontsize',16) set(h14,'color',[0.8 1 0.6]) h15=ylabel('deplasarea (m)'); set(h15,'fontname','times','fontsize',16) set(h15,'color',[0.3 0.6 0.5]) set(gca,'color',[0.8 0.2 0.8]) %calc max si min [zmax,imax]=max(z); [zmin,imin]=min(z); h16=text(t(imax)*1.10,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(t(imax))]) set(h16,'fontweight','bold') h17=text(t(imin+300),0.95*zmin,['minim=',num2str(zmin),'pentru t=',num2str(t(imin))]) set(h17,'fontweight','bold') set(h11,'Position',[150 50 600 500]) zp=(zp0*cos(omega*t)-omega*z0*sin(omega*t)); %raspunsul in viteze (m) h21=figure(2) plot(t,zp) set(h21,'color',[0.9 0 0.3]) set(h21,'name','Masterand Maria Solonaru, RCSC, an I') h22=plot(t,zp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h22(1),'color',[0.4 0.9 0.9]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.4 0 0.4]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspunsul liber neamortizat la impuls - viteze'); set(h23,'fontname','times','fontsize',16') set(h23,'color',[ 0.2 0.2 0.9]) h24=xlabel('timpul (t)'); set(h24,'fontname','times','fontsize',20) set(h24,'color',[ 0.4 0.2 0.5]) h25=ylabel('viteza m/s'); set(h25,'fontname','times','fontsize',18) set(h25,'color',[ 0.7 0.5 0.1])


Solonaru Maria

set(gca,'color',[0.9 0 0.6]) %calculul minimului si maximului [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h26=text(t(imax)*1.10,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(zp(imax))]) set(h26,'fontweight','bold') h27=text(t(imin)*1.10,0.95*zpmin,['minim=',num2str(zpmin),' pentru t=',num2str(zp(imin))]) set(h27,'fontweight','bold') zpp=-((omega^2)*z); %raspunsul in acceleratii(m/s^2) h31=figure(3) plot(t,zpp) set(h31,'color',[1 0.2 0.6]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(t,zpp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h32(1),'color',[0.4 0.7 1]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.9 0 0.4]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspunsul liber neamortizat la impuls - acceleratii'); set(h33,'fontname','times','fontsize',16') set(h33,'color',[ 0.2 0.2 0.7]) h34=xlabel('timpul (t)'); set(h34,'fontname','times','fontsize',20) set(h34,'color',[ 0.5 0.2 0.5]) h35=ylabel('acceleratia m/s^2'); set(h35,'fontname','times','fontsize',18) set(h35,'color',[ 0.3 0.1 0.1]) set(gca,'color',[0.8 0.4 1]) %calculul minimului si maximului [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h36=text(t(imax)*1.10,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(zpp(imax))]) set(h36,'fontweight','bold') h37=text(t(imin)*1.10,0.95*zppmin,['minim=',num2str(zppmin),' pentru t=',num2str(zpp(imin))]) set(h37,'fontweight','bold') h41=figure(4) %grafic comparativ set(h41,'color',[1 0.9 0.3]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') subplot(3,1,1) plot(t,z) subplot(3,1,2) plot(t,zp) subplot(3,1,3) plot(t,zpp) V=m*zpp h51=figure(5) %Graficul fortei taietoare plot(t,V); set(h51,'color',[0.8 0.2 0.7]); set(h51,'name','Masterand Maria Solonaru, RCSC, an I'); h52=plot(t,V,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h52(1),'color',[0.4 0.9 0.7]); set(h52(1),'linewidth',[2]); set(h52(2),'color',[0.8 0.2 0.4]); set(h52(2),'linewidth',[2]); set(h52(2),'linestyle','--'); h53=title('Graficul fortei taietoare'); set(h53,'fontname','times','fontsize',16') set(h53,'color',[ 0.1 0.2 0.7]); h54=xlabel('timpul (t)');


Solonaru Maria

set(h54,'fontname','times','fontsize',20) set(h54,'color',[ 0.6 0.9 0.1]); h55=ylabel('ft'); set(h55,'fontname','times','fontsize',18) set(h55,'color',[ 0.9 0.5 0.3]); set(gca,'color',[0.8 0.8 0.2]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h56=text(t(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(V(imax))]) set(h56,'fontweight','bold') h57=text(t(imin)*1.10,0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(V(imin))]) set(h57,'fontweight','bold') M=V*h h61=figure(6) %Graficul momentului incovoietor plot(t,M); set(h61,'color',[0.3 0.5 0.3]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(t,M,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h62(1),'color',[0.4 0.9 0.7]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.3 0.4 0.4]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul momentului incovoietor'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.3 0.9 0.1]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.5 0.8 0.1]); h65=ylabel('mi'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.7 0.1 0.9]); set(gca,'color',[0.2 0.5 0.6]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h66=text(t(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(M(imax))]) set(h66,'fontweight','bold') h67=text(t(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(M(imin))]) set(h67,'fontweight','bold') sigma =(M*hs)/(2*I) h71=figure(7) %Graficul efortului axial plot(t,sigma); set(h71,'color',[0.4 0.5 0.5]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(t,sigma,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h72(1),'color',[0.4 0.7 0.3]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.7 0.4 0.4]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul efortului axial'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.2 0.2 0.7]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.7 0.8 0.3]); h75=ylabel('sigma'); set(h75,'fontname','times','fontsize',18)


Solonaru Maria

set(h75,'color',[ 0.65 0.67 0.2]); set(gca,'color',[0.6 0.3 0.78]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h76=text(t(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(sigma(imax))]) set(h76,'fontweight','bold') h77=text(t(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(sigma(imin))]) set(h77,'fontweight','bold') tau =(V*hs^2)/(8*I) h81=figure(8) %Graficul efortului tangential plot(t,tau); set(h81,'color',[0.56 0.3 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(t,tau,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h82(1),'color',[0.1 0.4 0.3]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.9 0.3 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului tangential'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.6 0.9 0.6]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.43 0.7 0.7]); h85=ylabel('tau'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.6 0.3 0.9]); set(gca,'color',[0.7 0.2 0.0]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h86=text(t(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(tau(imax))]) set(h86,'fontweight','bold') h87=text(t(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(tau(imin))]) set(h87,'fontweight','bold')

2. Rezultate


Solonaru Maria




Solonaru Maria

% masterand Maria Solonaru close all clear all disp('Structuri cu 1GDL - raspuns liber amortizat - varianta 3') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii (cm)='); bs=bs/100; hs=input('inaltimea sectiunii (cm)='); hs=hs/100; m=input('masa (kg)='); niu=input('procentul din amortizarea critica (%)='); niu=niu/100; E=input('modulul de elasticitate(daN/cm^2)='); E=E*1e5; h=input('inaltimea grinzii (m)='); else bs=20; %latimea sectiunii bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) niu=5; %procentul din amortizarea critica (%) niu=niu/100; E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) end %calculul caracteristicilor geometrice %momentul de inertie (m^4) I=bs*hs^3/12; %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamice omega=sqrt(k/m); %pulsatia (rad/s) T=2*pi/omega; %perioada proprie de vibratia(s) f=1/T; % frecventa proprie (Hz) omegab=omega*sqrt(1-niu^2); %pulsatia in regim amortizzat Tb=T/sqrt(1-niu^2); % perioada de vibratie in regim amortizat fb=1/Tb; %raspunsul liber amortizat la impuls seismic al structurii cu 1GDL %conditii initiale upp=10; % acceleratie seismica instantanee m/s^2 pt=0.01;% pasul de timp H0=upp*m*pt; % kg*m/s impuls initial zp0=H0/m;% viteza initiala (m/s) %raspunsul liber amortizat t=0:0.1:5; %intervalul de timp al raspunsului z=(zp0/omegab*sin(omegab*t)).*exp(-niu*omega*t); %raspunsul in deplasari inf=zp0/omegab*exp(-niu*omega*t); h11=figure(1) set(h11,'name','Masterand Solonaru Maria, RCSC, an I') set(h11,'color',[0.4 0.6 0.2]) h12=plot(t,z,[0 t(end)],[0 0],'--',inf,-inf) set(gca,'color',[0.2 0.2 0.8]) set(h12(1),'color',[0.4 0.7 0])


Solonaru Maria

set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.8 0 0.5]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('Raspuns liber amortizat la impuls'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0.1 0.7 0.1]) h14=xlabel('timpul (s)'); set(h14,'fontname','times','fontsize',16) set(h14,'color',[0.3 0.6 0.6]) h15=ylabel('deplasarea (m)'); set(h15,'fontname','times','fontsize',16) set(h15,'color',[0.5 0.3 0.8]) set(gca,'color',[0.8 0.6 0.3]) %calc max si min [zmax,imax]=max(z); [zmin,imin]=min(z); h16=text(t(imax)*1.10,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(t(imax))]) set(h16,'fontweight','bold') h17=text(t(imin)*1.10,0.95*zmin,['minim=',num2str(zmin),'pentru t=',num2str(t(imin))]) set(h17,'fontweight','bold') set(h11,'Position',[150 50 600 500]) zp=zp0*cos(omegab*t).*exp(-niu*omega*t)-niu*omega*z; %raspunsul in viteze h21=figure(2) plot(t,zp) set(h21,'color',[0.9 0.1 0.3]) set(h21,'name','Masterand Maria Solonaru, RCSC, an I') h22=plot(t,zp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h22(1),'color',[0.5 0.4 0.7]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.2 0 0.4]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspunsul liber amortizat la impuls - viteze'); set(h23,'fontname','times','fontsize',16') set(h23,'color',[ 0.2 0.2 0.7]) h24=xlabel('timpul (t)'); set(h24,'fontname','times','fontsize',20) set(h24,'color',[ 0.9 0.6 0.1]) h25=ylabel('viteza m/s'); set(h25,'fontname','times','fontsize',18) set(h25,'color',[ 0.1 0.9 0.1]) set(gca,'color',[0 0.7 0.3]) %calculul minimului si maximului [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h26=text(t(imax)*1.10,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(zp(imax))]) set(h26,'fontweight','bold') h27=text(t(imin)*1.10,0.95*zpmin,['minim=',num2str(zpmin),' pentru t=',num2str(zp(imin))]) set(h27,'fontweight','bold') zpp=-2*niu*omega*zp-(omega^2)*z; %raspunsul in accelaratii h31=figure(3) plot(t,zpp) set(h31,'color',[0.0 0.5 1]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(t,zpp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h32(1),'color',[0.9 0.5 0.1]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.8 0.5 0.4]) set(h32(2),'linewidth',[2])


Solonaru Maria

set(h32(2),'linestyle','--') h33=title('Raspunsul liber amortizat la impuls - acceleratii'); set(h33,'fontname','times','fontsize',16') set(h33,'color',[ 0.2 0.2 0.7]) h34=xlabel('timpul (t)'); set(h34,'fontname','times','fontsize',20) set(h34,'color',[ 0.3 0.2 0.5]) h35=ylabel('acceleratia m/s^2'); set(h35,'fontname','times','fontsize',18) set(h35,'color',[ 0.4 0.9 0.1]) set(gca,'color',[0.9 0.2 0.6]) %calculul minimului si maximului [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h36=text(t(imax)*1.10,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(zpp(imax))]) set(h36,'fontweight','bold') h37=text(t(imin)*1.10,0.95*zppmin,['minim=',num2str(zppmin),' pentru t=',num2str(zpp(imin))]) set(h37,'fontweight','bold') h41=figure(4) %grafic comparativ set(h41,'color',[0.1 0.3 0.9]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') subplot(3,1,1) plot(t,z) subplot(3,1,2) plot(t,zp) subplot(3,1,3) plot(t,zpp) V=m*zpp h51=figure(5) %Graficul fortei taietoare plot(t,V); set(h51,'color',[0.7 0.2 0.3]); set(h51,'name','Masterand Maria Solonaru, RCSC, an I'); h52=plot(t,V,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h52(1),'color',[0.3 0.5 0.3]); set(h52(1),'linewidth',[2]); set(h52(2),'color',[0.1 0.4 0.4]); set(h52(2),'linewidth',[2]); set(h52(2),'linestyle','--'); h53=title('Graficul fortei taietoare'); set(h53,'fontname','times','fontsize',16') set(h53,'color',[ 0.1 0.2 0.7]); h54=xlabel('timpul (t)'); set(h54,'fontname','times','fontsize',20) set(h54,'color',[ 0.1 0.9 0.1]); h55=ylabel('ft'); set(h55,'fontname','times','fontsize',18) set(h55,'color',[ 0.2 0.1 0.1]); set(gca,'color',[0.4 0.1 0.6]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h56=text(t(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(V(imax))]) set(h56,'fontweight','bold') h57=text(t(imin)*1.10,0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(V(imin))]) set(h57,'fontweight','bold') M=V*h h61=figure(6) %Graficul momentului incovoietor plot(t,M); set(h61,'color',[0.7 0.3 0.3]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I');


Solonaru Maria

h62=plot(t,M,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h62(1),'color',[0.4 0.4 0]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.1 1 0.4]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul momentului incovoietor'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.5 0.9 0.3]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.4 0.9 0.1]); h65=ylabel('mi'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.9 0.4 0.1]); set(gca,'color',[0.3 1 0.6]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h66=text(t(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(M(imax))]) set(h66,'fontweight','bold') h67=text(t(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(M(imin))]) set(h67,'fontweight','bold') sigma =(M*hs)/(2*I) h71=figure(7) %Graficul efortului axial plot(t,sigma); set(h71,'color',[0.3 0.5 0.3]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(t,sigma,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h72(1),'color',[1 0 0]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.8 0 0.4]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul efortului axial'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.4 0.8 0.7]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.3 0.8 0.1]); h75=ylabel('sigma'); set(h75,'fontname','times','fontsize',18) set(h75,'color',[ 0.8 0.0 0.1]); set(gca,'color',[0.2 0.23 0.6]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h76=text(t(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(sigma(imax))]) set(h76,'fontweight','bold') h77=text(t(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(sigma(imin))]) set(h77,'fontweight','bold') tau =(V*hs^2)/(8*I) h81=figure(8) %Graficul efortului tangential plot(t,tau); set(h81,'color',[0.3 0.5 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(t,tau,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h82(1),'color',[0.3 0.5 0.6]); set(h82(1),'linewidth',[2]);


Solonaru Maria

set(h82(2),'color',[0.7 0.3 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului tangential'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.2 0.5 0.1]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.8 0.2 0.5]); h85=ylabel('tau'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.8 0.7 0.1]); set(gca,'color',[0.1 0.9 0.6]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h86=text(t(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(tau(imax))]) set(h86,'fontweight','bold') h87=text(t(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(tau(imin))]) set(h87,'fontweight','bold')

2. Rezultate


Solonaru Maria

PROBLEMA NR. 4 – FENOMENUL DE REZONANŢĂ

Rezonanţă – caz particular


Să se traseze grafice privind fenomenul de rezonanţă al structurilor cu un grad de libertate




În fizică, rezonanța este tendința unui sistem de a oscila cu amplitudine maximă la anumite

frecvențe, denumite frecvențe de rezonanță. La aceste frecvențe, chiar și forțe oscilante mici

pot produce amplitudini de vibrație mari, deoarece sistemul stochează energie oscilantă. Când


Solonaru Maria

atenuarea este mică, frecvența de rezonanță este aproximativ egală cu frecvența naturală a

sistemului, la care el vibrează liber.

Date de intrare:










3

12 𝑚4


𝛿 =1


2

2

3=

ℎ3

3𝐸𝐼

k – rigiditatea

𝑘 = 1/𝛿

ω – pulsaţia

𝜔 = 𝑘

𝑚

1 , 1

1 ∙ ℎ


Solonaru Maria


𝑇 =2𝜋

𝜔

f – frecvenţa

𝑓 =1

𝑇



% masterand Solonaru Maria,RCSC, an I close all clear all disp('Structuri cu 1GDL -Rezonanta - varianta 1') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii (cm)='); bs=bs/100; hs=input('inaltimea sectiunii (cm)='); hs=hs/100; m=input('masa (kg)='); niu=input('procentul din amortizarea critica (%)='); niu=niu/100; E=input('modulul de elasticitate(daN/cm^2)='); E=E*1e5; h=input('inaltimea grinzii (m)='); else bs=20; %latimea sectiunii (cm) bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) niu=5; %procentul din amortizarea critica (%) niu=niu/100; E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) end %calculul caracteristicilor geometrice %momentul de inertie (m^4) I=bs*hs^3/12; %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamice omega=sqrt(k/m); %pulsatia in regim neamortizat (rad/s) T=2*pi/omega; %perioada proprie de vibratie in regim neamortizat(s) f=1/T; % frecventa proprie (Hz) omegab=omega/sqrt(1-niu^2); %pulsatia in regim amortizat Tb=T*sqrt(1-niu^2); % perioada de vibratie in regim amortizat fb=1/Tb; %generare valori pt teta


Solonaru Maria

teta=0:0.01*omega:3*omega; p=teta/omega; % raportul pulsatiilor miu=1./sqrt((1-p.^2).^2+4*niu^2*p.^2); %coef de amplificare dinamica [miumax,imax]=max(miu) %generare valori pt teta tetab=0:0.01*omegab:3*omegab; pb=tetab/omegab; % raportul pulsatiilor miub=1./sqrt((1-pb.^2).^2+4*niu^2*pb.^2); %coef de amplificare dinamica [miubmax,imax]=max(miub) h11=figure(1); set(h11,'name','Masterand Solonaru Maria, RCSC, an I') set(h11,'color',[0.1 0.1 0.8]) h12=plot(p,miu,[1 1],[0 miumax*1.2]); set(gca,'color',[0.7 0.3 0.2]) set(h12(1),'color',[0.4 0.8 0.1]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.9 0.9 0.5]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('Rezonanta in regim liber neamortizat'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0.4 0 1]) h14=xlabel('p(teta/omega) '); set(h14,'fontname','times','fontsize',16) set(h14,'color',[0.2 1 0.6]) h15=ylabel('factor de amplificare dinamica (miu)'); set(h15,'fontname','times','fontsize',16) set(h15,'color',[0.7 0.2 0.8]) set(gca,'color',[0.9 0 0.8]) h21=figure(2); set(h21,'name','Masterand Solonaru Maria, RCSC, an I') set(h21,'color',[0.2 0.4 0.8]) h22=plot(pb,miub,[1 1],[0 miubmax*1.2]); set(gca,'color',[0.9 0.2 0.8]) set(h22(1),'color',[1 0.4 0.6]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.6 0.6 0.8]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Rezonanta in regim liber amortizat'); set(h23,'fontname','times','fontsize',18) set(h23,'color',[0.8 0.5 1]) h24=xlabel('pb(tetab/omegab) '); set(h24,'fontname','times','fontsize',16) set(h24,'color',[0.5 1 0.6]) h25=ylabel('factor de amplificare dinamica (miub)'); set(h25,'fontname','times','fontsize',16) set(h25,'color',[0.1 0.6 0.4]) set(gca,'color',[0.3 0.6 0.8])

4. Rezultate


Solonaru Maria

Rezonanţă – generalizare


% Masterand Solonaru Maria, RCSC, an I close all clear all disp('Structuri cu 1GDL - Rezonanata - varianta 2 - generalizare') % date de intrare %generare valori pt p p=0:0.01:3; % raportul pulsatiilor %generare interval valori pt amortizare niu=[1 3 5 10 29]/100; ngr=length(niu); %generare culori culori=[0.5 0.8 0.8;0.5 0.6 0.5;0.5 0.5 0.4;0.5 0.8 0.9;0.5 0.8 0.2] h11=figure(1); set(h11,'name','masterand Solonaru Maria, RCSC, an I') set(h11,'color',[0.2 0.2 0]) hold on for i=1:ngr miu=1./sqrt((1-p.^2).^2+4*niu(i)^2*p.^2); %coef de amplificare dinamica h12=plot(p,miu); set(gca,'color',[0.8 0.2 0.5]) set(h12(1),'color',culori(i,:)) set(h12(1),'linewidth',[2]) h16=text(2,max(miu)*0.5,['amortizare:',num2str(niu(i))]); end h13=title('Rezonanta-generalizare'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0.7 0.3 1]) h14=xlabel('p(teta/omega) '); set(h14,'fontname','times','fontsize',16) set(h14,'color',[0.9 0.8 0.6]) h15=ylabel('factor de amplificare dinamica (miu)'); set(h15,'fontname','times','fontsize',16) set(h15,'color',[0.3 0.7 0.8]) set(gca,'color',[0.8 0.3 0.8]) ax=axis;


Solonaru Maria

ax(4)=5*max(miu) axis(ax) h17=text(2,ax(4)*0.9,['amortizare: ',num2str(0)]) hold off [miumax,imax]=max(miu);

2. Rezultate

PROBLEMA NR. 5 – RĂSPUNSUL SEISMIC AL UNEI STRCUTURI CU 1GDL

Răspuns seism Vrancea în regim liber neamortizat – varianta 1




normal, efort unitar tangenţial şi un grafic comparativ al primelor trei, în baza înregistrărilor

seismului din Vrancea, 4 martie 1977.


Date de intrare:







Solonaru Maria





3

12 𝑚4


𝛿 =1


2

2

3=

ℎ3

3𝐸𝐼

k – rigiditatea

𝑘 = 1/𝛿

ω – pulsaţia

𝜔 = 𝑘

𝑚


𝑇 =2𝜋

𝜔

f – frecvenţa

𝑓 =1

𝑇


𝑚𝑧 𝑡 + 𝑘𝑧 𝑡 = 0


𝑧 𝑡 + 𝜔2𝑧 𝑡 = 0




𝜔sin(𝜔𝑡)






Solonaru Maria




𝑉 = 𝑚 ∙ 𝑧 (t)

𝑀 = 𝑉 ∙ ℎ

𝜎 =𝑀

𝐼·ℎ𝑠

2


𝐼 ∙ 𝑏𝑠



% masterand Maria Solonaru, RCSC, an I close all clear all disp('structuri cu 1GDL - raspuns seism Vrancea in regim liber neamortizat varianta 1') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii (cm)='); bs=bs/100; hs=input('inaltimea sectiunii (cm)='); hs=hs/100; m=input('masa (kg)='); E=input('modulul de elasticitate(daN/cm^2)='); E=E*1e5; h=input('inaltimea grinzii (m)='); else bs=20; %latimea sectiunii bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) end %calculul caracteristicilor geometrice %momentul de inertie (m^4) I=bs*hs^3/12; %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamice omega=sqrt(k/m); %pulsatia (rad/s)


Solonaru Maria

T=2*pi/omega; %perioada proprie de vibratia(s) f=1/T; % frecventa proprie (Hz) load VRAN.ACC [n,m]=size(VRAN); timp=0:0.02:(n-1)*0.02; estvest=VRAN(:,1); nordsud=VRAN(:,2); vertical=VRAN(:,3); [y1max,i1max]=max(nordsud); [y1min,i1min]=min(nordsud); h11=figure(1) set(h11,'color',[0.8 0.1 0.8]) set(h11,'name','Masterand Solonaru Maria, RCSC, an I') h12=plot(timp,nordsud,[0 timp(end)],[0,0]) set(h12(1),'color',[0.2 0.1 0.7]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.8 0.3 0.5]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.9 0.9 0.8]) h13=title('Seism Vrancea'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0.5 0.5 1]) %raspunsul liber neamortizat la impuls seismic al structurii cu 1 gdl %conditii initiale upp=10; %acceleratie seismica instantanee (m/s^2) pt=0.01 %pasul de timp H0=upp*m*pt; % impuls initial (kg*m/s) zp0=H0/m; %viteza initiala (m/s) %raspunsul liber neamortizat t=0:0.01:5; % intervalul de timp al raspunsului(s) z0=0 z=((zp0*sin(omega*t))/omega+z0*cos(omega*t)); %raspunsul in deplasari (m) inf=zp0/omega; h21=figure(2); plot(t,z) set(h21,'color',[0.9 0.7 0.3]) set(h21,'name','masterand Maria Solonaru, RCSC, an I') h22=plot(t,z,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h22(1),'color',[1 0.5 0]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.6 0.2 0.4]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspunsul liber amortizat la impuls'); set(h23,'fontname','times','fontsize',16') set(h23,'color',[ 0.2 0.2 0.7]) h24=xlabel('timpul (t)'); set(h24,'fontname','times','fontsize',20) set(h24,'color',[ 0.5 0.2 0.5]) h25=ylabel('deplasarea (m)'); set(h25,'fontname','times','fontsize',18) set(h25,'color',[ 0.9 0.5 0.1]) set(gca,'color',[0.6 0.8 0.6]) %calculul minimului si maximului


Solonaru Maria

[zmax,imax]=max(z); [zmin,imin]=min(z); h26=text(t(imax)*1.10,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(z(imax))]) set(h26,'fontweight','bold') h27=text(t(imin)*1.10,0.95*zmin,['minim=',num2str(zmin),' pentru t=',num2str(z(imin))]) set(h27,'fontweight','bold') set(h21,'Position',[150 50 600 500]) zp=(zp0*cos(omega*t)-omega*z0*sin(omega*t)); %raspunsul in viteze h31=figure(3) plot(t,zp) set(h31,'color',[0.3 0.2 0.3]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(t,zp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h32(1),'color',[1 0.6 0]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.8 1 0.4]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspunsul liber amortizat la impuls - viteze'); set(h33,'fontname','times','fontsize',16') set(h33,'color',[ 0.3 0.2 0.7]) h34=xlabel('timpul (t)'); set(h34,'fontname','times','fontsize',20) set(h34,'color',[ 0.6 0.2 0.5]) h35=ylabel('viteza m/s'); set(h35,'fontname','times','fontsize',18) set(h35,'color',[ 0.7 0.5 0.1]) set(gca,'color',[0.9 0.8 0.6]) %calculul minimului si maximului [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h36=text(t(imax)*1.10,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(zp(imax))]) set(h36,'fontweight','bold') h37=text(t(imin)*1.10,0.95*zpmin,['minim=',num2str(zpmin),' pentru t=',num2str(zp(imin))]) set(h37,'fontweight','bold') zpp=-((omega^2)*z); %raspunsul in accelaratii h41=figure(4) plot(t,zpp) set(h41,'color',[0.3 0.7 0.3]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') h42=plot(t,zpp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h42(1),'color',[0.7 0.5 0]) set(h42(1),'linewidth',[2]) set(h42(2),'color',[0.3 1 0.4]) set(h42(2),'linewidth',[2]) set(h42(2),'linestyle','--') h43=title('Raspunsul liber amortizat la impuls - acceleratii'); set(h43,'fontname','times','fontsize',16') set(h43,'color',[ 0.6 0.2 0.7]) h44=xlabel('timpul (t)'); set(h44,'fontname','times','fontsize',20) set(h44,'color',[ 0.8 0.2 0.5]) h45=ylabel('acceleratia m/s^2'); set(h45,'fontname','times','fontsize',18) set(h45,'color',[ 0.4 0.5 0.1]) set(gca,'color',[0.9 0.8 0.6]) %calculul minimului si maximului [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h46=text(t(imax)*1.10,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(zpp(imax))])


Solonaru Maria

set(h46,'fontweight','bold') h47=text(t(imin)*1.10,0.95*zppmin,['minim=',num2str(zppmin),' pentru t=',num2str(zpp(imin))]) set(h47,'fontweight','bold') h51=figure(5) %grafic comparativ set(h51,'color',[0.7 0.3 0.9]) set(h51,'name','Masterand Maria Solonaru, RCSC, an I') set(h51,'Position',[150 50 600 500]) subplot(4,1,2) plot(t,z) subplot(4,1,3) plot(t,zp) subplot(4,1,4) plot(t,zpp) V=m*zpp h61=figure(6) %Graficul fortei taietoare plot(t,V); set(h61,'color',[0.3 0.4 0.9]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(t,V,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h62(1),'color',[0.4 0.7 0.8]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.6 0.6 0.4]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul fortei taietoare'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.8 0.2 0.3]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.9 0.9 0.1]); h65=ylabel('ft'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.6 0.3 0.1]); set(gca,'color',[0.7 0.9 0.6]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h66=text(t(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(V(imax))]) set(h66,'fontweight','bold') h67=text(t(imin)*1.10,0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(V(imin))]) set(h67,'fontweight','bold') M=V*h h71=figure(7) %Graficul momentului incovoietor plot(t,M); set(h71,'color',[0.1 0.9 1]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(t,M,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h72(1),'color',[0.3 1 0]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.9 1 0.2]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul momentului incovoietor'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.8 0.8 0.3]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.0 0.7 0.4]); h75=ylabel('mi'); set(h75,'fontname','times','fontsize',18)


Solonaru Maria

set(h75,'color',[ 0.3 0.7 0.5]); set(gca,'color',[0.9 0.3 0.7]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h76=text(t(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(M(imax))]) set(h76,'fontweight','bold') h77=text(t(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(M(imin))]) set(h77,'fontweight','bold') sigma =(M*hs)/(2*I) h81=figure(8) %Graficul efortului axial plot(t,sigma); set(h81,'color',[0.9 0.3 0.5]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(t,sigma,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h82(1),'color',[0.6 0.5 0]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.8 0.5 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului axial'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.3 0.2 0.6]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.5 0.6 0.23]); h85=ylabel('sigma'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.98 0.1 0.1]); set(gca,'color',[0.98 0.7 0.43]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h86=text(t(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(sigma(imax))]) set(h86,'fontweight','bold') h87=text(t(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(sigma(imin))]) set(h87,'fontweight','bold') tau =(V*hs^2)/(8*I) h91=figure(9) %Graficul efortului tangential plot(t,tau); set(h91,'color',[0.4 0.7 0.23]); set(h91,'name','Masterand Maria Solonaru, RCSC, an I'); h92=plot(t,tau,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h92(1),'color',[0.65 0.3 0]); set(h92(1),'linewidth',[2]); set(h92(2),'color',[0.9 1 0.4]); set(h92(2),'linewidth',[2]); set(h92(2),'linestyle','--'); h93=title('Graficul efortului tangential'); set(h93,'fontname','times','fontsize',16') set(h93,'color',[ 0.4 0.9 0.1]); h94=xlabel('timpul (t)'); set(h94,'fontname','times','fontsize',20) set(h94,'color',[ 0.3 0.2 0.5]); h95=ylabel('tau'); set(h95,'fontname','times','fontsize',18) set(h95,'color',[ 0.2 0.7 0.8]); set(gca,'color',[0.9 0.23 0.7]); %calculul minimului si maximului


Solonaru Maria

[taumax,imax]=max(tau); [taumin,imin]=min(tau); h96=text(t(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(tau(imax))]) set(h96,'fontweight','bold') h97=text(t(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(tau(imin))]) set(h97,'fontweight','bold')

4. Rezultate


Solonaru Maria


Solonaru Maria

Răspuns seism Vrancea în regim liber amortizat – varianta 1





seismului din Vrancea, 4 martie 1977.


Date de intrare:










3

12 𝑚4


𝛿 =1


2

2

3=

ℎ3

3𝐸𝐼

k – rigiditatea

𝑘 = 1/𝛿

1 , 1

1 ∙ ℎ


Solonaru Maria

ω – pulsaţia

𝜔 = 𝑘

𝑚


𝑇 =2𝜋

𝜔

f – frecvenţa

𝑓 =1

𝑇




𝑧 𝑡 + 2𝜈𝜔𝑧 𝑡 + 𝜔2𝑧 𝑡 = 0











𝑧 𝑡 = −𝜔 2𝑧0 ∙ 𝑐𝑜𝑠 𝜔 𝑡 − 𝜔 2𝑧0 + 𝜈𝜔𝑧0










Solonaru Maria




𝑉 = 𝑚 ∙ 𝑧 (t)

𝑀 = 𝑉 ∙ ℎ

𝜎 =𝑀

𝐼·ℎ𝑠

2


𝐼 ∙ 𝑏𝑠


% masterand Maria Solonaru close all clear all disp('structuri cu 1GDL - raspuns seism Vrancea in regim liber amortizat-varianta1') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii (cm)='); bs=bs/100; hs=input('inaltimea sectiunii (cm)='); hs=hs/100; m=input('masa (kg)='); niu=input('procentul din amortizarea critica (%)='); niu=niu/100; E=input('modulul de elasticitate(daN/cm^2)='); E=E*1e5; h=input('inaltimea grinzii (m)='); else bs=20; %latimea sectiunii bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) niu=5; %procentul din amortizarea critica (%) niu=niu/100; E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) end %calculul caracteristicilor geometrice %momentul de inertie (m^4) I=bs*hs^3/12; %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamice omega=sqrt(k/m); %pulsatia (rad/s) T=2*pi/omega; %perioada proprie de vibratia(s)


Solonaru Maria

f=1/T; % frecventa proprie (Hz) omegab=omega*sqrt(1-niu^2); %pulsatia in regim amortizzat Tb=T/sqrt(1-niu^2); % perioada de vibratie in regim amortizat fb=1/Tb; load VRAN.ACC [n,m]=size(VRAN); timp=0:0.02:(n-1)*0.02; estvest=VRAN(:,1); nordsud=VRAN(:,2); vertical=VRAN(:,3); [y1max,i1max]=max(nordsud); [y1min,i1min]=min(nordsud); h11=figure(1) set(h11,'color',[0.8 0.2 0.8]) set(h11,'name','Masterand Solonaru Maria, RCSC, an I') h12=plot(timp,nordsud,[0 timp(end)],[0,0]) set(h12(1),'color',[0.3 0.4 0]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.9 0.6 0.5]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.3 0.5 0.8]) h13=title('Seism Vrancea'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0.3 0.8 1]) %raspunsul liber amortizat la impuls seismic al structurii cu 1 gdl %conditii initiale upp=10; %acceleratie seismica instantanee (m/s^2) pt=0.01 %pasul de timp H0=upp*m*pt; % impuls initial (kg*m/s) zp0=H0/m; %viteza initiala (m/s) %raspunsul liber si amortizat t=0:0.1:5; % intervalul de timp al raspunsului(s) z=(zp0/omegab*sin(omegab*t)).*exp(-niu*omega*t); %raspunsul in deplasari (m) inf=zp0/omegab*exp(-niu*omega*t); h21=figure(2); set(h21,'color',[0.2 0.2 0.3]) set(h21,'name','masterand Maria Solonaru, RCSC, an I') h22=plot(t,z,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h22(1),'color',[1 0.6 0.6]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.98 0.4 0.4]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspunsul liber amortizat la impuls'); set(h23,'fontname','times','fontsize',16') set(h23,'color',[ 0.3 0.2 0.23]) h24=xlabel('timpul (t)'); set(h24,'fontname','times','fontsize',20) set(h24,'color',[ 0.78 0.5 0.23]) h25=ylabel('deplasarea (m)'); set(h25,'fontname','times','fontsize',18) set(h25,'color',[ 0.54 0.6 0.1]) set(gca,'color',[0.2 0.90 0.6]) %calculul minimului si maximului


Solonaru Maria

[zmax,imax]=max(z); [zmin,imin]=min(z); h26=text(t(imax)*1.10,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(z(imax))]) set(h26,'fontweight','bold') h27=text(t(imin)*1.10,0.95*zmin,['minim=',num2str(zmin),' pentru t=',num2str(z(imin))]) set(h27,'fontweight','bold') set(h21,'Position',[150 50 600 500]) zp=zp0*cos(omegab*t).*exp(-niu*omega*t)-niu*omega*z; %raspunsul in viteze h31=figure(3) plot(t,zp) set(h31,'color',[0.9 0.43 0.234]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(t,zp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h32(1),'color',[0.23 0.54 0.9]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.8 0.43 0.23]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspunsul liber amortizat la impuls - viteze'); set(h33,'fontname','times','fontsize',16') set(h33,'color',[ 0.6 0.2 0.7]) h34=xlabel('timpul (t)'); set(h34,'fontname','times','fontsize',20) set(h34,'color',[ 0.8 0.2 0.5]) h35=ylabel('viteza m/s'); set(h35,'fontname','times','fontsize',18) set(h35,'color',[ 0.7 0.23 0.1]) set(gca,'color',[0.23 0.23 0.7]) %calculul minimului si maximului [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h36=text(t(imax)*1.10,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(zp(imax))]) set(h36,'fontweight','bold') h37=text(t(imin)*1.10,0.95*zpmin,['minim=',num2str(zpmin),' pentru t=',num2str(zp(imin))]) set(h37,'fontweight','bold') zpp=-2*niu*omega*zp-(omega^2)*z; %raspunsul in accelaratii h41=figure(4) plot(t,zpp) set(h41,'color',[0.9 0.243 0.43]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') h42=plot(t,zpp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h42(1),'color',[0 0.43 0.43]) set(h42(1),'linewidth',[2]) set(h42(2),'color',[0.23 0.54 0.243]) set(h42(2),'linewidth',[2]) set(h42(2),'linestyle','--') h43=title('Raspunsul liber amortizat la impuls - acceleratii'); set(h43,'fontname','times','fontsize',16') set(h43,'color',[ 0.23 0.90 0.7]) h44=xlabel('timpul (t)'); set(h44,'fontname','times','fontsize',20) set(h44,'color',[ 0.54 0.2 0.5]) h45=ylabel('acceleratia m/s^2'); set(h45,'fontname','times','fontsize',18) set(h45,'color',[ 0.98 0.6 0.1]) set(gca,'color',[0.23 0.068 0.6]) %calculul minimului si maximului [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h46=text(t(imax)*1.10,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(zpp(imax))])


Solonaru Maria

set(h46,'fontweight','bold') h47=text(t(imin)*1.10,0.95*zppmin,['minim=',num2str(zppmin),' pentru t=',num2str(zpp(imin))]) set(h47,'fontweight','bold') h51=figure(5) %grafic comparativ set(h51,'color',[0.23 0.43 0.8]) set(h51,'name','Masterand Maria Solonaru, RCSC, an I') set(h51,'Position',[150 50 600 500]) subplot(4,1,2) plot(t,z) subplot(4,1,3) plot(t,zp) subplot(4,1,4) plot(t,zpp) V=m*zpp h61=figure(6) %Graficul fortei taietoare plot(t,V); set(h61,'color',[0.98 0.24 0.5]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(t,V,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h62(1),'color',[0.5 0.5 0.54]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.43 0.6 0.4]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul fortei taietoare'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.8 0.43 0.7]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.78 0.54 0.1]); h65=ylabel('ft'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.54 0.90 0.1]); set(gca,'color',[0.35 0.78 0.2]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h66=text(t(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(V(imax))]) set(h66,'fontweight','bold') h67=text(t(imin)*1.10,0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(V(imin))]) set(h67,'fontweight','bold') M=V*h h71=figure(7) %Graficul momentului incovoietor plot(t,M); set(h71,'color',[0.178 0.23 0.3]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(t,M,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h72(1),'color',[1 0.43 0.23]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.43 0 0.4]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul momentului incovoietor'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.90 0.65 0.3]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.2 0.67 0.1]); h75=ylabel('mi'); set(h75,'fontname','times','fontsize',18)


Solonaru Maria

set(h75,'color',[ 0.64 0.1 0.68]); set(gca,'color',[0.4 0.8 0.9]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h76=text(t(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(M(imax))]) set(h76,'fontweight','bold') h77=text(t(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(M(imin))]) set(h77,'fontweight','bold') sigma =(M*hs)/(2*I) h81=figure(8) %Graficul efortului axial plot(t,sigma); set(h81,'color',[0.3 0.54 0.9]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(t,sigma,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h82(1),'color',[0 0.54 0.54]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.78 1 0.23]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului axial'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.243 0.234 0.7]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.53 0.789 0.9785]); h85=ylabel('sigma'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.243 0.64 0.9]); set(gca,'color',[0.685 0.56 0.978]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h86=text(t(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(sigma(imax))]) set(h86,'fontweight','bold') h87=text(t(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(sigma(imin))]) set(h87,'fontweight','bold') tau =(V*hs^2)/(8*I) h91=figure(9) %Graficul efortului tangential plot(t,tau); set(h91,'color',[0.9432 0.4355 0.54]); set(h91,'name','Masterand Maria Solonaru, RCSC, an I'); h92=plot(t,tau,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h92(1),'color',[0.1 0.65 0.54]); set(h92(1),'linewidth',[2]); set(h92(2),'color',[0.7 0.54 0.4]); set(h92(2),'linewidth',[2]); set(h92(2),'linestyle','--'); h93=title('Graficul efortului tangential'); set(h93,'fontname','times','fontsize',16') set(h93,'color',[ 0.5 0.243 0.243]); h94=xlabel('timpul (t)'); set(h94,'fontname','times','fontsize',20) set(h94,'color',[ 0.6 0.9 0.5]); h95=ylabel('tau'); set(h95,'fontname','times','fontsize',18) set(h95,'color',[ 0.4 0.54 0.1]); set(gca,'color',[0.943 0.234 0.6]); %calculul minimului si maximului


Solonaru Maria

[taumax,imax]=max(tau); [taumin,imin]=min(tau); h96=text(t(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(tau(imax))]) set(h96,'fontweight','bold') h97=text(t(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(tau(imin))]) set(h97,'fontweight','bold')

4. Rezultate


Solonaru Maria


Solonaru Maria

Răspuns seism Vrancea în regim liber neamortizat – varianta 2


% masterand Maria Solonaru close all clear all disp('structuri cu 1GDL - raspuns seism Vrancea liber neamortizat varianta 2') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii (cm)='); bs=bs/100; hs=input('inaltimea sectiunii (cm)='); hs=hs/100; m=input('masa (kg)='); niu=input('procentul din amortizarea critica (%)='); niu=niu/100; E=input('modulul de elasticitate(daN/cm^2)='); E=E*1e5; h=input('inaltimea grinzii (m)='); else bs=20; %latimea sectiunii bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) niu=5; %procentul din amortizarea critica (%) niu=niu/100; E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) end %calculul caracteristicilor geometrice %momentul de inertie (m^4) I=bs*hs^3/12; %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamice omega=sqrt(k/m); %pulsatia (rad/s) T=2*pi/omega; %perioada proprie de vibratia(s) f=1/T; % frecventa proprie (Hz) load VRAN.ACC [n,m]=size(VRAN); pt=0.02;% pasul de timp timp=0:pt:(n-1)*pt; nordsud=VRAN(:,2); [y1max,i1max]=max(nordsud); [y1min,i1min]=min(nordsud); h11=figure(1) set(h11,'color',[0.8 0.2 0.8]) set(h11,'name','Masterand Maria Solonaru, RCSC, anI') h12=plot(timp,nordsud,[0 timp(end)],[0,0]) set(h12(1),'color',[1 0.3 0.3]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.78 0.43 0.5]) set(h12(2),'linewidth',[2])


Solonaru Maria

set(h12(2),'linestyle','--') h13=title('Seism Vrancea'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0.43 0.243 1]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.789 0.53 0.8]) % iteratii pentru toti pasii de timp tau z=zeros(1,n); zp=zeros(1,n); zpp=zeros(1,n); for i=1:n tau=timp(i); %raspunsul liber neamortizat la impuls seismic al structurii cu 1GDL %conditii initiale upp=nordsud(i); % acceleratie seismica instantanee m/s^2 H0=upp*m*pt; % kg*m/s impuls initial zp0=H0/m;% viteza initiala (m/s) %raspunsul liber neamortizat t=tau:pt:timp(end); %intervalul de timp al raspunsului ztau=(zp0*sin(omega*(t-tau))/omega); %raspunsul in deplasari z(i:n)=z(i:n)+ztau; zptau=(zp0*cos(omega*(t-tau))); %raspunsul in viteze zp(i:n)=zp(i:n)+zptau; zpptau=(-(omega^2)*ztau); %raspunsul in accelaratii zpp(i:n)=zpp(i:n)+zpptau; end z=-z; h21=figure(2); plot(timp,z) set(h21,'name','masterand Solonaru Maria - RCSC an I') set(h21,'color',[0.97 0.43 0.8]) h22=plot(timp,z,[0 timp(end)],[0 0]) set(gca,'color',[0.34 0.243 0.8]) set(h22(1),'color',[0.23 0.67 0.43]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.8 0.2 0.5]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspuns seismic liber neamortizat-deplasari'); set(h23,'fontname','times','fontsize',18) set(h23,'color',[0.23 0.67 1]) h24=xlabel('timpul (s)'); set(h24,'fontname','times','fontsize',16) set(h24,'color',[0.8 1 0.6]) h25=ylabel('deplasarea (m)'); set(h25,'fontname','times','fontsize',16) set(h25,'color',[0.90 0.3 0.8]) set(gca,'color',[0.2 0.67 0.8]) %calc max si min [zmax,imax]=max(z); [zmin,imin]=min(z); h26=text(timp(imax)*1.10,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(timp(imax))]) set(h26,'fontweight','bold') h27=text(timp(imin+300),0.95*zmin,['minim=',num2str(zmin),'pentru t=',num2str(timp(imin))]) set(h27,'fontweight','bold') set(h21,'Position',[150 50 600 500])


Solonaru Maria

zp=-zp; h31=figure(3); plot(timp,zp) set(h31,'name','masterand Solonaru Maria - RCSC an I') set(h31,'color',[0.78 0.23 0.23]) h32=plot(timp,zp,[0 timp(end)],[0 0]) set(gca,'color',[0.76 0.23 0.23]) set(h32(1),'color',[0.43 0.4 0]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.8 0.23 0.23]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspuns seismic liber neamortizat-viteze'); set(h33,'fontname','times','fontsize',18) set(h33,'color',[1 0.43 0]) h34=xlabel('timpul (s)'); set(h34,'fontname','times','fontsize',16) set(h34,'color',[0 1 0.6]) h35=ylabel('viteza (s)'); set(h35,'fontname','times','fontsize',16) set(h35,'color',[0.23 0.6 0.8]) set(gca,'color',[0.78 0 0.8]) %calc max si min [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h36=text(timp(imax)*1.10,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(timp(imax))]) set(h36,'fontweight','bold') h37=text(timp(imin+300),0.95*zpmin,['minim=',num2str(zpmin),'pentru t=',num2str(timp(imin))]) set(h37,'fontweight','bold') set(h31,'Position',[150 50 600 500]) zpp=-zpp; h41=figure(4); plot(timp,zpp) set(h41,'name','masterand Solonaru Maria - RCSC an I') set(h41,'color',[0 0.8 0.23]) h42=plot(timp,zpp,[0 timp(end)],[0 0]) set(gca,'color',[0.1 0.23 0.8]) set(h42(1),'color',[1 0.2 0.4]) set(h42(1),'linewidth',[2]) set(h42(2),'color',[0.98 0.6 0.23]) set(h42(2),'linewidth',[2]) set(h42(2),'linestyle','--') h43=title('Raspuns seismic liber neamortizat-acceleratii'); set(h43,'fontname','times','fontsize',18) set(h43,'color',[0.3 0.5 1]) h44=xlabel('timpul (s)'); set(h44,'fontname','times','fontsize',16) set(h44,'color',[0.8 1 0.6]) h45=ylabel('acceleratie (m/s2)'); set(h45,'fontname','times','fontsize',16) set(h45,'color',[0.98 0.23 0.23]) set(gca,'color',[0.67 0.2 0.8]) %calc max si min [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h46=text(timp(imax)*1.10,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(timp(imax))]) set(h46,'fontweight','bold') h47=text(timp(imin+300),0.95*zppmin,['minim=',num2str(zppmin),'pentru t=',num2str(timp(imin))]) set(h47,'fontweight','bold') set(h41,'Position',[150 50 600 500])


Solonaru Maria

h51=figure(5) %grafic comparativ set(h51,'color',[0.23 0 0.3]) set(h51,'name','Masterand Maria Solonaru, RCSC, an I') set(h51,'Position',[150 50 600 500]) subplot(4,1,2) plot(timp,z) subplot(4,1,3) plot(timp,zp) subplot(4,1,4) plot(timp,zpp) V=m*zpp h61=figure(6) %Graficul fortei taietoare plot(timp,V); set(h61,'color',[0.67 0.23 0.3]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(timp,V,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h62(1),'color',[1 0.8 0.23]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.9 1 0.4]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul fortei taietoare'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.6 0.2 0.7]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.6 0.23 0.1]); h65=ylabel('ft'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.27 0.65 0.78]); set(gca,'color',[0.653 0.8 0.65]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h66=text(timp(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),'pentru t=',num2str(timp(imax))]) set(h66,'fontweight','bold') h67=text(timp(imin)*1.10,0.95*Vmin,['minim=',num2str(Vmin),'pentru t=',num2str(timp(imin))]) set(h67,'fontweight','bold') M=V*h h71=figure(7) %Graficul momentului incovoietor plot(timp,M); set(h71,'color',[0.11 0.78 0.3]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(timp,M,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h72(1),'color',[1 0.54 0.23]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.78 0.43 0.4]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul momentului incovoietor'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0 0.2 0.3]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',18) set(h74,'color',[ 0.54 0.43 0.43]); h75=ylabel('mi'); set(h75,'fontname','times','fontsize',18) set(h75,'color',[ 0.1 0.78 0.1]); set(gca,'color',[0.23 0.23 0.6]); %calculul minimului si maximului


Solonaru Maria

[Mmax,imax]=max(M); [Mmin,imin]=min(M); h76=text(timp(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(timp(imax))]) set(h76,'fontweight','bold') h77=text(timp(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(timp(imin))]) set(h77,'fontweight','bold') sigma =(M*hs)/(2*I) h81=figure(8) %Graficul efortului axial plot(timp,sigma); set(h81,'color',[0.23 0.43 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(timp,sigma,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h82(1),'color',[1 0.7 0]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.2 0.4 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului axial'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.6 0.2 0.7]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.1 0.54 0.1]); h85=ylabel('sigma'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.3 0.1 0.9]); set(gca,'color',[0.9 0.3 0.6]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h86=text(timp(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(timp(imax))]) set(h86,'fontweight','bold') h87=text(timp(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(timp(imin))]) set(h87,'fontweight','bold') tau =(V*hs^2)/(8*I) h91=figure(9) %Graficul efortului tangential plot(timp,tau); set(h91,'color',[0.7 0.88 0.3]); set(h91,'name','Masterand Maria Solonaru, RCSC, an I'); h92=plot(timp,tau,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h92(1),'color',[0.43 0.4 0]); set(h92(1),'linewidth',[2]); set(h92(2),'color',[0.2 1 0.4]); set(h92(2),'linewidth',[2]); set(h92(2),'linestyle','--'); h93=title('Graficul efortului tangential'); set(h93,'fontname','times','fontsize',16') set(h93,'color',[ 0.1 0.7 0.1]); h94=xlabel('timpul (t)'); set(h94,'fontname','times','fontsize',20) set(h94,'color',[ 0.3 0.2 0.5]); h95=ylabel('tau'); set(h95,'fontname','times','fontsize',18) set(h95,'color',[ 0.1 0.8 0.1]); set(gca,'color',[0.9 0.8 0.6]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau);


Solonaru Maria

h96=text(timp(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(timp(imax))]) set(h96,'fontweight','bold') h97=text(timp(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(timp(imin))]) set(h97,'fontweight','bold')

2. Rezultate


Solonaru Maria


Solonaru Maria

Răspuns seism Vrancea în regim liber amortizat – varianta 2


% masterand Maria Solonaru close all clear all disp('Structuri cu 1GDL - raspuns seism Vrancea in regim liber amortizat-varianta 2') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii (cm)='); bs=bs/100; hs=input('inaltimea sectiunii (cm)='); hs=hs/100; m=input('masa (kg)='); niu=input('procentul din amortizarea critica (%)='); niu=niu/100; E=input('modulul de elasticitate(daN/cm^2)='); E=E*1e5; h=input('inaltimea grinzii (m)='); else bs=20; %latimea sectiunii bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) niu=5; %procentul din amortizarea critica (%) niu=niu/100; E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) end %calculul caracteristicilor geometrice %momentul de inertie (m^4) I=bs*hs^3/12; %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamice omega=sqrt(k/m); %pulsatia (rad/s) T=2*pi/omega; %perioada proprie de vibratia(s) f=1/T; % frecventa proprie (Hz) omegab=omega*sqrt(1-niu^2); %pulsatia in regim amortizzat Tb=T/sqrt(1-niu^2); % perioada de vibratie in reg amortizat fb=1/Tb; load VRAN.ACC [n,m]=size(VRAN); pt=0.02;% pasul de timp timp=0:pt:(n-1)*pt; nordsud=VRAN(:,2); [y1max,i1max]=max(nordsud); [y1min,i1min]=min(nordsud); h11=figure(1) set(h11,'color',[0.2 0.3 0.8]) set(h11,'name','Masterand Solonaru Maria, RCSC, an I') h12=plot(timp,nordsud,[0 timp(end)],[0,0]) set(h12(1),'color',[0.43 0.54 0.78])


Solonaru Maria

set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.78 0.9 0.234]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('Seism Vrancea'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0.9 0.54 0.23]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.7 0.43 0.43]) % iteratii pentru toti pasii de timp tau z=zeros(1,n); zp=zeros(1,n); zpp=zeros(1,n); for i=1:n tau=timp(i); %raspunsul liber amortizat la impuls seismic al structurii cu 1GDL %conditii initiale upp=nordsud(i); % acceleratie seismica instantanee m/s^2 H0=upp*m*pt; % kg*m/s impuls initial zp0=H0/m;% viteza initiala (m/s) %raspunsul liber amortizat t=tau:pt:timp(end); %intervalul de timp al raspunsului ztau=(zp0/omegab*sin(omegab*(t-tau))).*exp(-niu*omega*(t-tau)); %raspunsul in deplasari z(i:n)=z(i:n)+ztau; zptau=zp0*cos(omegab*(t-tau)).*exp(-niu*omega*(t-tau))-niu*omega*ztau; %raspunsul in viteze zp(i:n)=zp(i:n)+zptau; zpptau=-2*niu*omega*zptau-(omega^2)*ztau; %raspunsul in accelaratii zpp(i:n)=zpp(i:n)+zpptau; end z=-z; h21=figure(2); plot(timp,z) set(h21,'name','masterand Solonaru Maria - RCSC an I') set(h21,'color',[0.98 0.65 0.54]) h22=plot(timp,z,[0 timp(end)],[0 0]) set(gca,'color',[0.90 0.23 0.43]) set(h22(1),'color',[0.23 0.54 0.2]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[1 0.54 1]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspuns seismic liber amortizat-deplasari'); set(h23,'fontname','times','fontsize',18) set(h23,'color',[0.43 0.43 1]) h24=xlabel('timpul (s)'); set(h24,'fontname','times','fontsize',16) set(h24,'color',[0.8 0 0.6]) h25=ylabel('deplasarea (m)'); set(h25,'fontname','times','fontsize',16) set(h25,'color',[0.2 0.7 0.28]) set(gca,'color',[0.98 0.2 0.2]) %calc max si min [zmax,imax]=max(z); [zmin,imin]=min(z); h26=text(timp(imax)*1.10,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(timp(imax))]) set(h26,'fontweight','bold')


Solonaru Maria

h27=text(timp(imin+300),0.95*zmin,['minim=',num2str(zmin),'pentru t=',num2str(timp(imin))]) set(h27,'fontweight','bold') set(h21,'Position',[150 50 600 500]) zp=-zp; h31=figure(3); plot(timp,zp) set(h31,'name','masterand Solonaru Maria - RCSC an I') set(h31,'color',[0.6 0.2 0.1]) h32=plot(timp,zp,[0 timp(end)],[0 0]) set(gca,'color',[0.2 0.3 0.8]) set(h32(1),'color',[0.43 0.4 0]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0 0.67 0.54]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspuns seismic liber amortizat-viteze'); set(h33,'fontname','times','fontsize',18) set(h33,'color',[0.3 0.23 1]) h34=xlabel('timpul (s)'); set(h34,'fontname','times','fontsize',16) set(h34,'color',[0.432 1 0.6]) h35=ylabel('viteza (s)'); set(h35,'fontname','times','fontsize',16) set(h35,'color',[0.43 0.6 0.8]) set(gca,'color',[0.9 0.43 0.8]) %calc max si min [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h36=text(timp(imax)*1.10,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(timp(imax))]) set(h36,'fontweight','bold') h37=text(timp(imin+300),0.95*zpmin,['minim=',num2str(zpmin),'pentru t=',num2str(timp(imin))]) set(h37,'fontweight','bold') set(h31,'Position',[150 50 600 500]) zpp=-zpp; h41=figure(4); plot(timp,zpp) set(h41,'name','masterand Solonaru Maria - RCSC an I') set(h41,'color',[0.9 0.23 0.2]) h42=plot(timp,zpp,[0 timp(end)],[0 0]) set(gca,'color',[0.8 0.1 0.1]) set(h42(1),'color',[0.43 0.67 0.2]) set(h42(1),'linewidth',[2]) set(h42(2),'color',[0.8 0.23 0.67]) set(h42(2),'linewidth',[2]) set(h42(2),'linestyle','--') h43=title('Raspuns seismic liber amortizat-acceleratii'); set(h43,'fontname','times','fontsize',18) set(h43,'color',[0.23 0.43 0.43]) h44=xlabel('timpul (s)'); set(h44,'fontname','times','fontsize',16) set(h44,'color',[0.43 0.3 0.6]) h45=ylabel('acceleratie (m/s2)'); set(h45,'fontname','times','fontsize',16) set(h45,'color',[0.43 0.67 0.78]) set(gca,'color',[0.9 0.43 0.43]) %calc max si min [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h46=text(timp(imax)*1.10,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(timp(imax))]) set(h46,'fontweight','bold')


Solonaru Maria

h47=text(timp(imin+300),0.95*zppmin,['minim=',num2str(zppmin),'pentru t=',num2str(timp(imin))]) set(h47,'fontweight','bold') set(h41,'Position',[150 50 600 500]) h51=figure(5) %grafic comparativ set(h51,'color',[0.1 0.67 0]) set(h51,'name','Masterand Maria Solonaru, RCSC, an I') set(h51,'Position',[150 50 600 500]) subplot(4,1,2) plot(timp,z) subplot(4,1,3) plot(timp,zp) subplot(4,1,4) plot(timp,zpp) V=m*zpp h61=figure(6) %Graficul fortei taietoare plot(timp,V); set(h61,'color',[0.9 0 0.3]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(timp,V,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h62(1),'color',[0.54 0.3 0]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.01 0.43 0.6]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul fortei taietoare'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.54 0.2 0.7]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.65 0.65 0.1]); h65=ylabel('ft'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.43 0.90 0.1]); set(gca,'color',[0.09 0.8 0.67]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h66=text(timp(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(timp(imax))]) set(h66,'fontweight','bold') h67=text(timp(imin+300),0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(timp(imin))]) set(h67,'fontweight','bold') M=V*h h71=figure(7) %Graficul momentului incovoietor plot(timp,M); set(h71,'color',[0.19 0.43 0.9]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(timp,M,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h72(1),'color',[0.54 0.5 0.67]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.8 0.43 0.4]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul momentului incovoietor'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.2 0.8 0.3]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.3 0.9 0.1]); h75=ylabel('mi'); set(h75,'fontname','times','fontsize',18)


Solonaru Maria

set(h75,'color',[ 0.2 0.8 0.1]); set(gca,'color',[0.9 0.9 0.6]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h76=text(timp(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(timp(imax))]) set(h76,'fontweight','bold') h77=text(timp(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(timp(imin))]) set(h77,'fontweight','bold') sigma =(M*hs)/(2*I) h81=figure(8) %Graficul efortului axial plot(timp,sigma); set(h81,'color',[0.7 0.77 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(timp,sigma,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h82(1),'color',[1 0.4 0.8]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.2 1 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului axial'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.43 0.78 0.7]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.16 0.19 0.7]); h85=ylabel('sigma'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.1 0.98 0.685]); set(gca,'color',[0.9657 0.6 0.6]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h86=text(timp(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(timp(imax))]) set(h86,'fontweight','bold') h87=text(timp(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(timp(imin))]) set(h87,'fontweight','bold') tau =(V*hs^2)/(8*I) h91=figure(9) %Graficul efortului tangential plot(timp,tau); set(h91,'color',[0.99 0.80 0.3]); set(h91,'name','Masterand Maria Solonaru, RCSC, an I'); h92=plot(timp,tau,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h92(1),'color',[1 0.54 0.43]); set(h92(1),'linewidth',[2]); set(h92(2),'color',[1 0.4 0.4]); set(h92(2),'linewidth',[2]); set(h92(2),'linestyle','--'); h93=title('Graficul efortului tangential'); set(h93,'fontname','times','fontsize',16') set(h93,'color',[ 0.23 0.98 0.1]); h94=xlabel('timpul (t)'); set(h94,'fontname','times','fontsize',20) set(h94,'color',[ 0.67 0.2 0.5]); h95=ylabel('tau'); set(h95,'fontname','times','fontsize',18) set(h95,'color',[ 0.98 0.65 0.1]); set(gca,'color',[0.78 0.9 0.6]);


Solonaru Maria

%calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h96=text(timp(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(timp(imax))]) set(h96,'fontweight','bold') h97=text(timp(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(timp(imin))]) set(h97,'fontweight','bold')

2. Rezultate


Solonaru Maria


Solonaru Maria

Răspuns seism Lytle Creek în regim liber amortizat





seismului din Lytle Creek, 12 septembrie 1970.


% masterand Maria Solonaru close all clear all disp('Structuri cu 1GDL - raspuns seism Lytle Creek in regim liber amortizat') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii (cm)='); bs=bs/100; hs=input('inaltimea sectiunii (cm)='); hs=hs/100; m=input('masa (kg)='); niu=input('procentul din amortizarea critica (%)='); niu=niu/100; E=input('modulul de elasticitate(daN/cm^2)='); E=E*1e5; h=input('inaltimea grinzii (m)='); else bs=20; %latimea sectiunii bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) niu=5; %procentul din amortizarea critica (%) niu=niu/100; E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) end %calculul caracteristicilor geometrice %momentul de inertie (m^4) I=bs*hs^3/12; %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamice omega=sqrt(k/m); %pulsatia (rad/s) T=2*pi/omega; %perioada proprie de vibratia(s) f=1/T; % frecventa proprie (Hz) omegab=omega*sqrt(1-niu^2); %pulsatia in regim amortizzat Tb=T/sqrt(1-niu^2); % perioada de vibratie in reg amortizat


Solonaru Maria

fb=1/Tb; load LYTLE.ACC [n,m]=size(LYTLE); pt=0.2;% pasul de timp timp=0:pt:(n-1)*pt; nordsud=LYTLE(:,1); [y1max,i1max]=max(nordsud); [y1min,i1min]=min(nordsud); h11=figure(1) set(h11,'color',[0.67 0.1 0.8]) set(h11,'name','Masterand Solonaru Maria, RCSC, an I') h12=plot(timp,nordsud,[0 timp(end)],[0,0]) set(h12(1),'color',[1 0.43 0.23]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.98 0.43 0.5]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('Seism Lytle Creek'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0.43 0.7 1]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.75 0.2 0.8]) % iteratii pentru toti pasii de timp tau z=zeros(1,n); zp=zeros(1,n); zpp=zeros(1,n); for i=1:n tau=timp(i); %raspunsul liber amortizat la impuls seismic al structurii cu 1GDL %conditii initiale upp=nordsud(i); % acceleratie seismica instantanee m/s^2 H0=upp*m*pt; % kg*m/s impuls initial zp0=H0/m;% viteza initiala (m/s) %raspunsul liber amortizat t=tau:pt:timp(end); %intervalul de timp al raspunsului ztau=(zp0/omegab*sin(omegab*(t-tau))).*exp(-niu*omega*(t-tau)); %raspunsul in deplasari z(i:n)=z(i:n)+ztau; zptau=zp0*cos(omegab*(t-tau)).*exp(-niu*omega*(t-tau))-niu*omega*ztau; %raspunsul in viteze zp(i:n)=zp(i:n)+zptau; zpptau=-2*niu*omega*zptau-(omega^2)*ztau; %raspunsul in accelaratii zpp(i:n)=zpp(i:n)+zpptau; end z=-z; h21=figure(2); plot(timp,z) set(h21,'name','masterand Solonaru Maria - RCSC an I') set(h21,'color',[0.1 0.45 0.8]) h22=plot(timp,z,[0 timp(end)],[0 0]) set(gca,'color',[0.54 0 0.65]) set(h22(1),'color',[0.32 0.23 0.43]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.7 0.23 0.5]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspuns seismic liber amortizat-deplasari'); set(h23,'fontname','times','fontsize',18)


Solonaru Maria

set(h23,'color',[0.3 0.5 1]) h24=xlabel('timpul (s)'); set(h24,'fontname','times','fontsize',16) set(h24,'color',[0.4 0.3 0.6]) h25=ylabel('deplasarea (m)'); set(h25,'fontname','times','fontsize',16) set(h25,'color',[0.9 0.1 0.8]) set(gca,'color',[0.3 1 0.8]) %calc max si min [zmax,imax]=max(z); [zmin,imin]=min(z); h26=text(timp(imax)*1.10,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(timp(imax))]) set(h26,'fontweight','bold') h27=text(timp(imin)*1.10,0.95*zmin,['minim=',num2str(zmin),'pentru t=',num2str(timp(imin))]) set(h27,'fontweight','bold') set(h21,'Position',[150 50 600 500]) zp=-zp; h31=figure(3); plot(timp,zp) set(h31,'name','masterand Solonaru Maria - RCSC an I') set(h31,'color',[0.2 0.2 0.8]) h32=plot(timp,zp,[0 timp(end)],[0 0]) set(gca,'color',[0.7 0.2 0.8]) set(h32(1),'color',[1 0.6 0]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.2 1 0.2]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspuns seismic liber amortizat-viteze'); set(h33,'fontname','times','fontsize',18) set(h33,'color',[0.54 0.2 0.76]) h34=xlabel('timpul (s)'); set(h34,'fontname','times','fontsize',16) set(h34,'color',[0.87 1 0.6]) h35=ylabel('viteza (s)'); set(h35,'fontname','times','fontsize',16) set(h35,'color',[0.23 0.23 0.8]) set(gca,'color',[0.78 0.54 0.8]) %calc max si min [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h36=text(timp(imax)*1.10,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(timp(imax))]) set(h36,'fontweight','bold') h37=text(timp(imin)*1.10,0.95*zpmin,['minim=',num2str(zpmin),'pentru t=',num2str(timp(imin))]) set(h37,'fontweight','bold') set(h31,'Position',[150 50 600 500]) zpp=-zpp; h41=figure(4); plot(timp,zpp) set(h41,'name','masterand Solonaru Maria - RCSC an I') set(h41,'color',[0.3 0.8 0.8]) h42=plot(timp,zpp,[0 timp(end)],[0 0]) set(gca,'color',[1 0.67 0.8]) set(h42(1),'color',[1 0.6 0.67]) set(h42(1),'linewidth',[2]) set(h42(2),'color',[0.98 0.54 0.78]) set(h42(2),'linewidth',[2]) set(h42(2),'linestyle','--') h43=title('Raspuns seismic liber amortizat-acceleratii'); set(h43,'fontname','times','fontsize',18)


Solonaru Maria

set(h43,'color',[0.4 0.67 1]) h44=xlabel('timpul (s)'); set(h44,'fontname','times','fontsize',16) set(h44,'color',[0.23 1 0.6]) h45=ylabel('acceleratie (m/s2)'); set(h45,'fontname','times','fontsize',16) set(h45,'color',[0.67 0.98 0.8]) set(gca,'color',[0.23 0.43 0.8]) %calc max si min [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h46=text(timp(imax)*1.10,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(timp(imax))]) set(h46,'fontweight','bold') h47=text(timp(imin)*1.10,0.95*zppmin,['minim=',num2str(zppmin),'pentru t=',num2str(timp(imin))]) set(h47,'fontweight','bold') set(h41,'Position',[150 50 600 500]) h51=figure(5) %grafic comparativ set(h51,'color',[0.98 0.23 0.3]) set(h51,'name','Masterand Maria Solonaru, RCSC, an I') set(h51,'Position',[150 50 600 500]) subplot(4,1,2) plot(timp,z) subplot(4,1,3) plot(timp,zp) subplot(4,1,4) plot(timp,zpp) V=m*zpp h61=figure(6) %Graficul fortei taietoare plot(timp,V); set(h61,'color',[0.23 0.43 0.23]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(timp,V,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h62(1),'color',[0.43 0.78 0.98]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.2 1 0.4]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul fortei taietoare'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.6 0.98 0.7]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.4 0.54 0.1]); h65=ylabel('ft'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.23 0.678 0.78]); set(gca,'color',[0.90 0.43 0.6]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h66=text(timp(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(timp(imax))]) set(h66,'fontweight','bold') h67=text(timp(imin)*1.10,0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(timp(imin))]) set(h67,'fontweight','bold') M=V*h h71=figure(7) %Graficul momentului incovoietor plot(timp,M); set(h71,'color',[0.1 0.65 0.78]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(timp,M,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf);


Solonaru Maria

set(h72(1),'color',[0.4 0.67 0.54]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.78 1 1]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul momentului incovoietor'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.23 0.67 0.98]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.23 0.54 0.1]); h75=ylabel('mi'); set(h75,'fontname','times','fontsize',18) set(h75,'color',[ 0.78 0.65 0.82]); set(gca,'color',[0.8 0.7 0.6]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h76=text(timp(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(timp(imax))]) set(h76,'fontweight','bold') h77=text(timp(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(timp(imin))]) set(h77,'fontweight','bold') sigma =(M*hs)/(2*I) h81=figure(8) %Graficul efortului axial plot(timp,sigma); set(h81,'color',[0 0.7 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(timp,sigma,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h82(1),'color',[0.54 0.65 0.2]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.1 1 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului axial'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.98 0.2 0.7]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.67 0.67 0.90]); h85=ylabel('sigma'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.43 0.98 0.1]); set(gca,'color',[0.98 0.8 0.6]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h86=text(timp(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(timp(imax))]) set(h86,'fontweight','bold') h87=text(timp(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(timp(imin))]) set(h87,'fontweight','bold') tau =(V*hs^2)/(8*I) h91=figure(9) %Graficul efortului tangential plot(timp,tau); set(h91,'color',[0.67 0.3 0.3]); set(h91,'name','Masterand Maria Solonaru, RCSC, an I'); h92=plot(timp,tau,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h92(1),'color',[0.3 0.4 0.1]); set(h92(1),'linewidth',[2]);


Solonaru Maria

set(h92(2),'color',[0.2 0.5 0.8]); set(h92(2),'linewidth',[2]); set(h92(2),'linestyle','--'); h93=title('Graficul efortului tangential'); set(h93,'fontname','times','fontsize',16') set(h93,'color',[ 0.8 0.3 0.9]); h94=xlabel('timpul (t)'); set(h94,'fontname','times','fontsize',20) set(h94,'color',[ 0.65 0.2 0.5]); h95=ylabel('tau'); set(h95,'fontname','times','fontsize',18) set(h95,'color',[ 0.98 0.1 0.1]); set(gca,'color',[0.43 0.8 0.6]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h96=text(timp(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(timp(imax))]) set(h96,'fontweight','bold') h97=text(timp(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(timp(imin))]) set(h97,'fontweight','bold')

3. Rezultate


Solonaru Maria


Solonaru Maria

Răspuns seism Near E. Coast of Honshu, Japan în regim liber amortizat





seismului Honshu, Japonia.


% masterand Maria Solonaru close all clear all disp('Structuri cu 1GDL - raspuns seism Near E. Coast of Honshu, Japan in regim liber amortizat') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii (cm)='); bs=bs/100; hs=input('inaltimea sectiunii (cm)='); hs=hs/100; m=input('masa (kg)='); niu=input('procentul din amortizarea critica (%)='); niu=niu/100; E=input('modulul de elasticitate(daN/cm^2)='); E=E*1e5; h=input('inaltimea grinzii (m)='); else bs=20; %latimea sectiunii bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) niu=5; %procentul din amortizarea critica (%) niu=niu/100; E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) end %calculul caracteristicilor geometrice %momentul de inertie (m^4) I=bs*hs^3/12; %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamice omega=sqrt(k/m); %pulsatia (rad/s) T=2*pi/omega; %perioada proprie de vibratia(s) f=1/T; % frecventa proprie (Hz) omegab=omega*sqrt(1-niu^2); %pulsatia in regim amortizzat Tb=T/sqrt(1-niu^2); % perioada de vibratie in reg amortizat fb=1/Tb; load NEAR.ACC [n,m]=size(NEAR);


Solonaru Maria

pt=0.02;% pasul de timp timp=0:pt:(n-1)*pt; nordsud=NEAR(:,2); [y1max,i1max]=max(nordsud); [y1min,i1min]=min(nordsud); h11=figure(1) set(h11,'color',[0.7 0.43 0.8]) set(h11,'name','Masterand Solonaru Maria, RCSC, an I') h12=plot(timp,nordsud,[0 timp(end)],[0,0]) set(h12(1),'color',[1 0.43 0.23]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.23 0.6 0.98]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('Seism Near E. Coast of Honshu, Japan'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0.23 0.978 0.5]) ax=axis; ax(2)=timp(end); ax(3)=y1min*1.1; ax(4)=y1max*1.1; axis(ax); set(gca,'color',[0.7 0.54 0.23]) % iteratii pentru toti pasii de timp tau z=zeros(1,n); zp=zeros(1,n); zpp=zeros(1,n); for i=1:n tau=timp(i); %raspunsul liber amortizat la impuls seismic al structurii cu 1GDL %conditii initiale upp=nordsud(i); % acceleratie seismica instantanee m/s^2 H0=upp*m*pt; % kg*m/s impuls initial zp0=H0/m;% viteza initiala (m/s) %raspunsul liber amortizat t=tau:pt:timp(end); %intervalul de timp al raspunsului ztau=(zp0/omegab*sin(omegab*(t-tau))).*exp(-niu*omega*(t-tau)); %raspunsul in deplasari z(i:n)=z(i:n)+ztau; zptau=zp0*cos(omegab*(t-tau)).*exp(-niu*omega*(t-tau))-niu*omega*ztau; %raspunsul in viteze zp(i:n)=zp(i:n)+zptau; zpptau=-2*niu*omega*zptau-(omega^2)*ztau; %raspunsul in accelaratii zpp(i:n)=zpp(i:n)+zpptau; end z=-z; h21=figure(2); plot(timp,z) set(h21,'name','masterand Solonaru Maria - RCSC an I') set(h21,'color',[0.98 0.23 0.2]) h22=plot(timp,z,[0 timp(end)],[0 0]) set(gca,'color',[0.21 0.3 0.8]) set(h22(1),'color',[0.54 0.4 0.67]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.78 0.978 0.5]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspuns seismic liber amortizat-deplasari'); set(h23,'fontname','times','fontsize',18) set(h23,'color',[0 0.968 1]) h24=xlabel('timpul (s)'); set(h24,'fontname','times','fontsize',16)


Solonaru Maria

set(h24,'color',[0.98 0 0.6]) h25=ylabel('deplasarea (m)'); set(h25,'fontname','times','fontsize',16) set(h25,'color',[0.2 0.54 0.8]) set(gca,'color',[0.76 0.98 0.21]) %calc max si min [zmax,imax]=max(z); [zmin,imin]=min(z); h26=text(timp(imax)*1.10,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(timp(imax))]) set(h26,'fontweight','bold') h27=text(timp(imin)*1.10,0.95*zmin,['minim=',num2str(zmin),'pentru t=',num2str(timp(imin))]) set(h27,'fontweight','bold') set(h21,'Position',[150 50 600 500]) zp=-zp; h31=figure(3); plot(timp,zp) set(h31,'name','masterand Solonaru Maria - RCSC an I') set(h31,'color',[0.234 0.23 0.8]) h32=plot(timp,zp,[0 timp(end)],[0 0]) set(gca,'color',[0.78 0.54 0.8]) set(h32(1),'color',[0.65 0.6 0.54]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.2 0.78 0.5]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspuns seismic liber amortizat-viteze'); set(h33,'fontname','times','fontsize',18) set(h33,'color',[0.43 0.988 1]) h34=xlabel('timpul (s)'); set(h34,'fontname','times','fontsize',16) set(h34,'color',[0.785 1 0.6]) h35=ylabel('viteza (s)'); set(h35,'fontname','times','fontsize',16) set(h35,'color',[0.432 0.6 0.43]) set(gca,'color',[0.98 0.24 0.78]) %calc max si min [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h36=text(timp(imax)*1.10,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(timp(imax))]) set(h36,'fontweight','bold') h37=text(timp(imin)*1.10,0.95*zpmin,['minim=',num2str(zpmin),'pentru t=',num2str(timp(imin))]) set(h37,'fontweight','bold') set(h31,'Position',[150 50 600 500]) zpp=-zpp; h41=figure(4); plot(timp,zpp) set(h41,'name','masterand Solonaru Maria - RCSC an I') set(h41,'color',[0.98 0.43 0.8]) h42=plot(timp,zpp,[0 timp(end)],[0 0]) set(gca,'color',[0.21 0.23 0.8]) set(h42(1),'color',[1 0.54 0]) set(h42(1),'linewidth',[2]) set(h42(2),'color',[0.5 0.23 0]) set(h42(2),'linewidth',[2]) set(h42(2),'linestyle','--') h43=title('Raspuns seismic liber amortizat-acceleratii'); set(h43,'fontname','times','fontsize',18) set(h43,'color',[1 0.785 1]) h44=xlabel('timpul (s)'); set(h44,'fontname','times','fontsize',16)


Solonaru Maria

set(h44,'color',[0.3 1 0.6]) h45=ylabel('acceleratie (m/s2)'); set(h45,'fontname','times','fontsize',16) set(h45,'color',[0.67 0.6 0.8]) set(gca,'color',[0.2 0.78 0.2]) %calc max si min [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h46=text(timp(imax)*1.10,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(timp(imax))]) set(h46,'fontweight','bold') h47=text(timp(imin)*1.10,0.95*zppmin,['minim=',num2str(zppmin),'pentru t=',num2str(timp(imin))]) set(h47,'fontweight','bold') set(h41,'Position',[150 50 600 500]) h51=figure(5) %grafic comparativ set(h51,'color',[0.1 0.23 0.3]) set(h51,'name','Masterand Maria Solonaru, RCSC, an I') set(h51,'Position',[150 50 600 500]) subplot(4,1,2) plot(timp,z) subplot(4,1,3) plot(timp,zp) subplot(4,1,4) plot(timp,zpp) V=m*zpp h61=figure(6) %Graficul fortei taietoare plot(timp,V); set(h61,'color',[0.8 0.54 0.3]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(timp,V,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h62(1),'color',[1 0.54 0.4]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.90 1 0.4]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul fortei taietoare'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.23 0.65 0.7]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.8 0.98 0]); h65=ylabel('ft'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.90 0.67 0.23]); set(gca,'color',[0.65 0.78 0.6]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h66=text(timp(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(timp(imax))]) set(h66,'fontweight','bold') h67=text(timp(imin)*1.10,0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(timp(imin))]) set(h67,'fontweight','bold') M=V*h h71=figure(7) %Graficul momentului incovoietor plot(timp,M); set(h71,'color',[0.43 0.78 0.98]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(timp,M,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h72(1),'color',[1 0.65 0.67]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.78 0.43 0.4]);


Solonaru Maria

set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul momentului incovoietor'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.23 0.78 0.3]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.98 0.78 0.1]); h75=ylabel('mi'); set(h75,'fontname','times','fontsize',18) set(h75,'color',[ 0.134 0.67 0.1]); set(gca,'color',[0.67 0.785 0.6]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h76=text(timp(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(timp(imax))]) set(h76,'fontweight','bold') h77=text(timp(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(timp(imin))]) set(h77,'fontweight','bold') sigma =(M*hs)/(2*I) h81=figure(8) %Graficul efortului axial plot(timp,sigma); set(h81,'color',[0.98 0.2 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(timp,sigma,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h82(1),'color',[1 0 0]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.5 1 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului axial'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.1 0.2 0.7]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.3 0.8 0.1]); h85=ylabel('sigma'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.78 0.787 0.1]); set(gca,'color',[0.9 0.65 0.65]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h86=text(timp(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(timp(imax))]) set(h86,'fontweight','bold') h87=text(timp(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(timp(imin))]) set(h87,'fontweight','bold') tau =(V*hs^2)/(8*I) h91=figure(9) %Graficul efortului tangential plot(timp,tau); set(h91,'color',[0.32 0.54 0.3]); set(h91,'name','Masterand Maria Solonaru, RCSC, an I'); h92=plot(timp,tau,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h92(1),'color',[0 0.78 0.4]); set(h92(1),'linewidth',[2]); set(h92(2),'color',[0.2 0.43 0.4]); set(h92(2),'linewidth',[2]); set(h92(2),'linestyle','--');


Solonaru Maria

h93=title('Graficul efortului tangential'); set(h93,'fontname','times','fontsize',16') set(h93,'color',[ 0.8 0.78 0.1]); h94=xlabel('timpul (t)'); set(h94,'fontname','times','fontsize',20) set(h94,'color',[ 0.9 0.43 0.5]); h95=ylabel('tau'); set(h95,'fontname','times','fontsize',18) set(h95,'color',[ 0.43 0.8 0.1]); set(gca,'color',[0.90 0 0.2]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h96=text(timp(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(timp(imax))]) set(h96,'fontweight','bold') h97=text(timp(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(timp(imin))]) set(h97,'fontweight','bold')

3. Rezultate


Solonaru Maria


Solonaru Maria

PROBLEMA NR. 6

Calculul structurilor cu 1 GDL în regim liber neamortizat


Date de intrare:










3

12 𝑚4


𝛿 =1


2

2

3=

ℎ3

3𝐸𝐼

k – rigiditatea

𝑘 = 1/𝛿

ω – pulsaţia

1 , 1

1 ∙ ℎ


Solonaru Maria

𝜔 = 𝑘

𝑚


𝑇 =2𝜋

𝜔

f – frecvenţa

𝑓 =1

𝑇


𝑚𝑧 𝑡 + 𝑘𝑧 𝑡 = 0 care poate fi scrisă astfel:

𝑧 𝑡 + 𝜔2𝑧 𝑡 = 0




𝜔sin(𝜔𝑡)








𝑉 = 𝑚 ∙ 𝑧 (t)

𝑀 = 𝑉 ∙ ℎ

𝜎 =𝑀

𝐼·ℎ𝑠

2


𝐼 ∙ 𝑏𝑠


Solonaru Maria


% Masterand Solonaru Maria, RCSC, an I close all clear all disp('structuri cu 1GDL -raspuns liber neamortizat') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii (cm)='); bs=bs/100; hs=input('inaltimea sectiunii (cm)='); hs=hs/100; m=input('masa (kg)='); E=input('modulul de elasticitate(daN/cm^2)='); E=E*1e5; h=input('inaltimea grinzii (m)='); else bs=20; %latimea sectiunii bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) %calculul caracteristicilor geometrice %momentul de inertie (m^4) I=bs*hs^3/12; end %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamica omega=sqrt(k/m); %pulsatia (rad/s) T=2*pi/omega; %perioada proprie de vibratia(s) f=1/T; % frecventa proprie (Hz) %raspunsul liber al structurii cu 1GDL %conditii initiale z0=5; %deplasarea initiala (cm) z0=z0/100; % m zp0=2000;%viteza initiala (cm/s) zp0=zp0/100; %m/s t=0:0.01:5; %intervalul de timp al raspunsului mt=t(end); z=z0*cos(omega*t)+(zp0*sin(omega*t))/omega; %raspunsul in deplasari h11=figure(1); set(h11,'color',[0.8 0.234 0.23]) h12=plot(t,z,[0 mt],[0 0]); set(h12(1),'color',[0.54 0.65 0.43]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.2 0.23 0.5]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('Raspuns liber neamortizat in deplasari'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0 0.43 1]) h14=xlabel('timpul (s)');


Solonaru Maria

set(h14,'fontname','times','fontsize',16) set(h14,'color',[0.43 0 0.6]) h15=ylabel('deplasare (m)'); set(h15,'fontname','times','fontsize',16) set(h15,'color',[0.2 0.785 0.8]) set(gca,'color',[0 0.543 0.98]) %calculul minimului si maximului [zmax,imax]=max(z); [zmin,imin]=min(z); h16=text(t(imax)*0.8,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(z(imax))]) set(h16,'fontweight','bold') h17=text(t(imin)*0.8,0.95*zmin,['minim=',num2str(zmin),' pentru t=',num2str(z(imin))]) set(h17,'fontweight','bold') zp=-omega*z0*sin(omega*t)+zp0*cos(omega*t) %raspunsul in viteze h21=figure(2) plot(t,zp) set(h21,'color',[0.98 0.5 0.3]) set(h21,'name','Masterand Maria Solonaru, RCSC, an I') h22=plot(t,zp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h22(1),'color',[0.4 0.43 0.23]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.98 0.54 0.4]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspunsul liber neamortizat in viteze'); set(h23,'fontname','times','fontsize',16') set(h23,'color',[ 0.6 0.29 0.43]) h24=xlabel('timpul (t)'); set(h24,'fontname','times','fontsize',20) set(h24,'color',[ 0.98 0.2 0.785]) h25=ylabel('viteza m/s'); set(h25,'fontname','times','fontsize',18) set(h25,'color',[ 0.43 0.542 0.431]) set(gca,'color',[0.21 0.78 0.65]) %calculul minimului si maximului [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h26=text(t(imax)*0.8,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(zp(imax))]) set(h26,'fontweight','bold') h27=text(t(imin)*0.8,0.95*zpmin,['minim=',num2str(zpmin),' pentru t=',num2str(zp(imin))]) set(h27,'fontweight','bold') zpp=-(omega^2)*z; %raspunsul in accelaratii h31=figure(3) plot(t,zpp) set(h31,'color',[0.968 0.43 0.3]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(t,zpp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h32(1),'color',[0.4 0.5 0.54]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.98 1 0]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspunsul liber neamortizat in acceleratii'); set(h33,'fontname','times','fontsize',16') set(h33,'color',[ 0 0.65 0.7]) h34=xlabel('timpul (t)'); set(h34,'fontname','times','fontsize',20) set(h34,'color',[ 0.67 0.2 0.5]) h35=ylabel('acceleratia m/s^2'); set(h35,'fontname','times','fontsize',18)


Solonaru Maria

set(h35,'color',[ 0.98 0.5 0.1]) set(gca,'color',[0.2 0.8 0.6]) %calculul minimului si maximului [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h36=text(t(imax)*0.8,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(zpp(imax))]) set(h36,'fontweight','bold') h37=text(t(imin)*0.8,0.95*zppmin,['minim=',num2str(zppmin),' pentru t=',num2str(zpp(imin))]) set(h37,'fontweight','bold') h41=figure(4) %grafic comparativ set(h41,'color',[0.78 0.43 0.3]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') subplot(3,1,1) plot(t,z) subplot(3,1,2) plot(t,zp) subplot(3,1,3) plot(t,zpp) V=m*zpp h51=figure(5) %Graficul fortei taietoare plot(t,V); set(h51,'color',[0.33 0.43 0.3]); set(h51,'name','Masterand Maria Solonaru, RCSC, an I'); h52=plot(t,V,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h52(1),'color',[1 0.43 0.2]); set(h52(1),'linewidth',[2]); set(h52(2),'color',[0.8 1 0.2]); set(h52(2),'linewidth',[2]); set(h52(2),'linestyle','--'); h53=title('Graficul fortei taietoare'); set(h53,'fontname','times','fontsize',16') set(h53,'color',[ 0.4 0.2 0.7]); h54=xlabel('timpul (t)'); set(h54,'fontname','times','fontsize',20) set(h54,'color',[ 0.78 0.8 0.23]); h55=ylabel('ft'); set(h55,'fontname','times','fontsize',18) set(h55,'color',[ 0.65 0.65 0.23]); set(gca,'color',[0.908 0.78 0.6]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h56=text(t(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(V(imax))]) set(h56,'fontweight','bold') h57=text(t(imin)*1.10,0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(V(imin))]) set(h57,'fontweight','bold') M=V*h h61=figure(6) %Graficul momentului incovoietor plot(t,M); set(h61,'color',[0.11 0.67 0.67]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(t,M,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h62(1),'color',[0.54 0.67 0.67]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.908 1 0.43]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul momentului incovoietor'); set(h63,'fontname','times','fontsize',16')


Solonaru Maria

set(h63,'color',[ 0.54 0.8 0.98]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.78 0.89 0.98]); h65=ylabel('mi'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.98 0.54 0.90]); set(gca,'color',[0.90 0.90 0.6]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h66=text(t(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(M(imax))]) set(h66,'fontweight','bold') h67=text(t(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(M(imin))]) set(h67,'fontweight','bold') sigma =(M*hs)/(2*I) h71=figure(7) %Graficul efortului axial plot(t,sigma); set(h71,'color',[0.23 0.790 0.3]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(t,sigma,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h72(1),'color',[1 0.78 0.3]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.23 1 0.4]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul efortului axial'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.90 0.2 0.7]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.43 0.897 0.1]); h75=ylabel('sigma'); set(h75,'fontname','times','fontsize',18) set(h75,'color',[ 0.67 0.78 0.1]); set(gca,'color',[0.43 0.0 0.6]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h76=text(t(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(sigma(imax))]) set(h76,'fontweight','bold') h77=text(t(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(sigma(imin))]) set(h77,'fontweight','bold') tau =(V*hs^2)/(8*I) h81=figure(8) %Graficul efortului tangential plot(t,tau); set(h81,'color',[0.4354 0.658 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(t,tau,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h82(1),'color',[1 0.54 0.23]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.5 0.23 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului tangential'); set(h83,'fontname','times','fontsize',16')


Solonaru Maria

set(h83,'color',[ 0.5 0.43 0.9]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.9 0.2 0.5]); h85=ylabel('tau'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.66 0.9 0.1]); set(gca,'color',[0.234 0.23 0.6]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h86=text(t(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(tau(imax))]) set(h86,'fontweight','bold') h87=text(t(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(tau(imin))]) set(h87,'fontweight','bold')

3. Rezultate


Solonaru Maria

Calculul structurilor cu 1 GDL în regim liber amortizat


Date de intrare:







Solonaru Maria





3

12 𝑚4


𝛿 =1


2

2

3=

ℎ3

3𝐸𝐼

k – rigiditatea

𝑘 = 1/𝛿

ω – pulsaţia

𝜔 = 𝑘

𝑚


𝑇 =2𝜋

𝜔

f – frecvenţa

𝑓 =1

𝑇




𝑧 𝑡 + 2𝜈𝜔𝑧 𝑡 + 𝜔2𝑧 𝑡 = 0







Solonaru Maria






𝑧 𝑡 = −𝜔 2𝑧0 ∙ 𝑐𝑜𝑠 𝜔 𝑡 − 𝜔 2𝑧0 + 𝜈𝜔𝑧0












𝑉 = 𝑚 ∙ 𝑧 (t)

𝑀 = 𝑉 ∙ ℎ

𝜎 =𝑀

𝐼·ℎ𝑠

2


𝐼 ∙ 𝑏𝑠


% Masterand Solonaru Maria, RCSC, an I close all clear all disp('structuri cu 1GDL- raspuns liber amortizat') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii (cm)='); bs=bs/100; hs=input('inaltimea sectiunii (cm)='); hs=hs/100; m=input('masa (kg)='); niu=input('procentul din amortizarea critica (%)='); niu=niu/100; E=input('modulul de elasticitate(daN/cm^2)='); E=E*1e5; h=input('inaltimea grinzii (m)=');


Solonaru Maria

else bs=20; %latimea sectiunii bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) niu=5; %procentul din amortizarea critica (%) niu=niu/100; E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) %calculul caracteristicilor geometrice %momentul de inertie (m^4) I=bs*hs^3/12; end %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamice omega=sqrt(k/m); %pulsatia (rad/s) T=2*pi/omega; %perioada proprie de vibratia(s) f=1/T; % frecventa proprie (Hz) omegab=omega*sqrt(1-niu^2); %pulsatia in regim amortizat Tb=T/sqrt(1-niu^2); % perioada de vibratie in regim amortizat fb=1/Tb; %raspunsul liber amortizat al structurii cu 1GDL %conditii initiale z0=5; %deplasarea initiala (cm) z0=z0/100; % m zp0=200;%viteza initiala (cm/s) zp0=zp0/100; %m/s %raspunsul liber amortizat t=0:0.01:5; %intervalul de timp al raspunsului z=(z0*cos(omegab*t)+((zp0+niu*omega*z0)/omegab)*sin(omegab*t)).*exp(-niu*omega*t); %raspunsul in deplasari h11=figure(1) set(h11,'name','masterand Solonaru Maria - RCSC an I') set(h11,'color',[0.78 0.23 0.243]) inf=sqrt(z0^2+((zp0+niu*omega*z0)/omegab)^2).*exp(-niu*omega*t); h12=plot(t,z,[0 t(end)],[0 0],'--',inf,-inf) set(gca,'color',[0.67 0.23 0.67]) set(h12(1),'color',[0.43 0.5 0.4]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.78 0.2 0.789]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('Raspuns liber amortizat'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0.3 0.78 0]) h14=xlabel('timpul (s)'); set(h14,'fontname','times','fontsize',16) set(h14,'color',[0.67 1 0.6]) h15=ylabel('deplasarea (m)'); set(h15,'fontname','times','fontsize',16) set(h15,'color',[0.54 0.6 0.78]) set(gca,'color',[0.2 0.78 0.98]) %calc max si min [zmax,imax]=max(z);


Solonaru Maria

[zmin,imin]=min(z); h16=text(t(imax)*1.10,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(t(imax))]) set(h16,'fontweight','bold') h17=text(t(imin),0.95*zmin,['minim=',num2str(zmin),'pentru t=',num2str(t(imin))]) set(h17,'fontweight','bold') set(h11,'Position',[150 50 600 500]) zp=(-omegab*z0*sin(omegab*t)+zp0*cos(omegab*t).*exp(-niu*omega*t)-(niu*omega*(zp0+niu*omega*z0)/omegab)*sin(omegab*t).*exp(-niu*omega*t)); %raspunsul in viteze h21=figure(2) plot(t,zp) set(h21,'color',[0.98 0.4 0.43]) set(h21,'name','Masterand Maria Solonaru, RCSC, an I') h22=plot(t,zp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h22(1),'color',[1 0.54 0.56]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.3 1 0.4]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspunsul liber amortizat in viteze'); set(h23,'fontname','times','fontsize',16') set(h23,'color',[ 0.4 0.2 0.7]) h24=xlabel('timpul (t)'); set(h24,'fontname','times','fontsize',20) set(h24,'color',[ 0.1 0.9 0.5]) h25=ylabel('viteza m/s'); set(h25,'fontname','times','fontsize',18) set(h25,'color',[ 0.6 0.5 0.9]) set(gca,'color',[0.2 0.8 0.6]) %calculul minimului si maximului [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h26=text(t(imax)*0.8,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(zp(imax))]) set(h26,'fontweight','bold') h27=text(t(imin)*0.8,0.95*zpmin,['minim=',num2str(zpmin),' pentru t=',num2str(zp(imin))]) set(h27,'fontweight','bold') zpp=-2*niu*omega*zp-omega^2*z; %raspunsul in accelaratii h31=figure(3) plot(t,zpp) set(h31,'color',[0.9 0 0.3]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(t,zpp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h32(1),'color',[0.3 0.1 0]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.75 1 0.4]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspunsul liber amortizat in acceleratii'); set(h33,'fontname','times','fontsize',16') set(h33,'color',[ 0.2 0.34 0.7]) h34=xlabel('timpul (t)'); set(h34,'fontname','times','fontsize',20) set(h34,'color',[ 0.67 0.2 0.5]) h35=ylabel('acceleratia m/s^2'); set(h35,'fontname','times','fontsize',18) set(h35,'color',[ 0.7 0 0.1]) set(gca,'color',[0.2 0.1 0.6]) %calculul minimului si maximului [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h36=text(t(imax)*0.8,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(zpp(imax))])


Solonaru Maria

set(h36,'fontweight','bold') h37=text(t(imin)*0.8,0.95*zppmin,['minim=',num2str(zppmin),' pentru t=',num2str(zpp(imin))]) set(h37,'fontweight','bold') h41=figure(4) %grafic comparativ set(h41,'color',[0.9 0 0.3]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') subplot(3,1,1) plot(t,z) subplot(3,1,2) plot(t,zp) subplot(3,1,3) plot(t,zpp) V=m*zpp h51=figure(5) %Graficul fortei taietoare plot(t,V); set(h51,'color',[0.33 0.7 0.3]); set(h51,'name','Masterand Maria Solonaru, RCSC, an I'); h52=plot(t,V,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h52(1),'color',[1 0.78 0.3]); set(h52(1),'linewidth',[2]); set(h52(2),'color',[0.98 0.54 0.4]); set(h52(2),'linewidth',[2]); set(h52(2),'linestyle','--'); h53=title('Graficul fortei taietoare'); set(h53,'fontname','times','fontsize',16') set(h53,'color',[ 0.43 0.2 0.7]); h54=xlabel('timpul (t)'); set(h54,'fontname','times','fontsize',20) set(h54,'color',[ 0.54 0.98 0.1]); h55=ylabel('ft'); set(h55,'fontname','times','fontsize',18) set(h55,'color',[ 0.98 0.78 0.1]); set(gca,'color',[1 0.98 0.6]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h56=text(t(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(V(imax))]) set(h56,'fontweight','bold') h57=text(t(imin)*1.10,0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(V(imin))]) set(h57,'fontweight','bold') M=V*h h61=figure(6) %Graficul momentului incovoietor plot(t,M); set(h61,'color',[0.11 0.7 0.3]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(t,M,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h62(1),'color',[1 0.67 0.7]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.5 0.54 0.4]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul momentului incovoietor'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.43 0.98 0.3]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.234 0.43 0.87]); h65=ylabel('mi'); set(h65,'fontname','times','fontsize',18)


Solonaru Maria

set(h65,'color',[ 0.65 0.78 0.90]); set(gca,'color',[0.23 0.65 0.9]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h66=text(t(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(M(imax))]) set(h66,'fontweight','bold') h67=text(t(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(M(imin))]) set(h67,'fontweight','bold') sigma =(M*hs)/(2*I) h71=figure(7) %Graficul efortului axial plot(t,sigma); set(h71,'color',[0.43 0.77 0.3]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(t,sigma,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h72(1),'color',[1 0.653 0]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0 0.54 0.4]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul efortului axial'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.43 0.655 0.7]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.787 0.8 0.78]); h75=ylabel('sigma'); set(h75,'fontname','times','fontsize',18) set(h75,'color',[ 0.54 0.98 0.1]); set(gca,'color',[0.1 0.9 0.78]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h76=text(t(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(sigma(imax))]) set(h76,'fontweight','bold') h77=text(t(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(sigma(imin))]) set(h77,'fontweight','bold') tau =(V*hs^2)/(8*I) h81=figure(8) %Graficul efortului tangential plot(t,tau); set(h81,'color',[0 0.788 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(t,tau,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h82(1),'color',[1 0.65 0.54]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.78 0.65 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului tangential'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.43 0.65 0.21]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.21 0.2 0.5]); h85=ylabel('tau'); set(h85,'fontname','times','fontsize',18)


Solonaru Maria

set(h85,'color',[ 0.98 0.1 0.1]); set(gca,'color',[0.23 0.8 0.6]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h86=text(t(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(tau(imax))]) set(h86,'fontweight','bold') h87=text(t(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(tau(imin))]) set(h87,'fontweight','bold')

3. Rezultate


Solonaru Maria

Calculul structurilor cu 1 GDL în regim forţat amortizat


Date de intrare:







Solonaru Maria





3

12 𝑚4


𝛿 =1


2

2

3=

ℎ3

3𝐸𝐼

k – rigiditatea

𝑘 = 1/𝛿

ω – pulsaţia

𝜔 = 𝑘

𝑚


𝑇 =2𝜋

𝜔

f – frecvenţa

𝑓 =1

𝑇


𝑚𝑧 𝑡 + 𝑐𝑧 𝑡 + 𝑘𝑧 𝑡 = 𝐹0𝑠𝑖𝑛θt


𝑧 𝑡 = 𝜇𝛿𝐹0𝑠𝑖𝑛𝜃𝑡


𝑧 𝑡 = 𝜇𝛿𝐹0𝜃𝑐𝑜𝑠𝜃𝑡


𝑧 𝑡 = −𝜇𝛿𝐹0𝜃2𝑠𝑖𝑛𝜃𝑡 = −𝜃2𝑧(𝑡)


θ – pulsaţia forţei perturbatoare armonice

𝑝 =𝜃

𝜔


Solonaru Maria

𝜇 =1

(1 − 𝑝2)2 + 4𝜈2𝑝2

μ – factor de amplificare dinamică, care ţine cont de amortizare

F0 sinθt – forţa perturbatoare



𝑉 = 𝑚 ∙ 𝑧 (t)

𝑀 = 𝑉 ∙ ℎ

𝜎 =𝑀

𝐼·ℎ𝑠

2


𝐼 ∙ 𝑏𝑠


% Masterand Solonaru Maria, RCSC, an I close all clear all disp('structuri cu 1GDL - raspuns fortat') % date de intrare int=0; %daca int=1 se lucreaza interactiv if int==1 bs=input('latimea sectiunii (cm)='); bs=bs/100; hs=input('inaltimea sectiunii (cm)='); hs=hs/100; m=input('masa (kg)='); niu=input('procentul din amortizarea critica (%)='); niu=niu/100; E=input('modulul de elasticitate(daN/cm^2)='); E=E*1e5; h=input('inaltimea grinzii (m)='); teta=input('pulsatia fortei perturbatoare armonice (rad/s) =') F0=input('amplitudinea fortei perturbatoare armonice (KN)=') F0=F0*1000; else bs=20; %latimea sectiunii bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) niu=5; %procentul din amortizarea critica (%) niu=niu/100; E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) teta=8; %pulsatia fortei perturbatoare armonice (rad/s)


Solonaru Maria

F0=3e6; %amplitudinea fortei perturbatoare armonice (KN) %calculul caracteristicilor gveometrice %momentul de inertie (m^4) I=bs*hs^3/12; end %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamice omega=sqrt(k/m); %pulsatia (rad/s) T=2*pi/omega; %perioada proprie de vibratia(s) f=1/T; % frecventa proprie (Hz) omegab=omega/sqrt(1-niu^2); %pulsatia in regim amortizat Tb=T*sqrt(1-niu^2); % perioada de vibratie in reg amortizat fb=1/Tb; %raspunsul fortat amortizat al structurii cu 1GDL %conditii initiale z0=5; %deplasarea initiala (cm) z0=z0/100; % m zp0=200;%viteza initiala (cm/s) zp0=zp0/100; %m/s %raspunsul fortat amortizat t=0:0.01:5; %intervalul de timp al raspunsului (s) p=teta/omega; % raportul pulsatiilor miu=1/sqrt((1-p^2)^2+4*niu^2*p^2); %coef de amplificare dinamica z=miu*F0*delta*sin(teta*t); %raspunsul in deplasari h11=figure(1) set(h11,'name','masterand Solonaru Maria - RCSC an I') set(h11,'color',[0.1 0.3 0.8]) inf=sqrt(miu*F0*delta); h12=plot(t,z,[0 t(end)],[0 0],'--') set(gca,'color',[0.32 0.78 0.8]) set(h12(1),'color',[1 0.65 0.54]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.43 0.23 0.2]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('Raspuns amortizat fortat'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0.43 0.5 0.87]) h14=xlabel('timpul (s)'); set(h14,'fontname','times','fontsize',16) set(h14,'color',[0.43 0.2 0.6]) h15=ylabel('deplasarea (m)'); set(h15,'fontname','times','fontsize',16) set(h15,'color',[0.23 0.6 0.8]) %calculul minimului si maximului [zmax,imax]=max(z); [zmin,imin]=min(z); h16=text(t(imax)*0.8,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(z(imax))]) set(h16,'fontweight','bold') h17=text(t(imin)*0.8,0.95*zmin,['minim=',num2str(zmin),' pentru t=',num2str(z(imin))]) set(h17,'fontweight','bold') set(gca,'color',[0.78 0.65 0.8]) zp=teta*miu*F0*delta*cos(teta*t); %raspunsul in viteze (m) h21=figure(2) plot(t,zp) set(h21,'color',[0.978 0.98 0.3])


Solonaru Maria

set(h21,'name','Masterand Maria Solonaru, RCSC, an I') h22=plot(t,zp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h22(1),'color',[0.3 0.54 0.4]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.98 0 0.4]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspunsul liber amortizat in viteze'); set(h23,'fontname','times','fontsize',16') set(h23,'color',[ 0.653 0.2 0.7]) h24=xlabel('timpul (t)'); set(h24,'fontname','times','fontsize',20) set(h24,'color',[ 0.67 0.2 0.5]) h25=ylabel('viteza m/s'); set(h25,'fontname','times','fontsize',18) set(h25,'color',[ 0.23 0.5 0.65]) set(gca,'color',[0.1 0.65 0.988]) %calculul minimului si maximului [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h26=text(t(imax)*0.8,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(zp(imax))]) set(h26,'fontweight','bold') h27=text(t(imin)*0.8,0.95*zpmin,['minim=',num2str(zpmin),' pentru t=',num2str(zp(imin))]) set(h27,'fontweight','bold') zpp=-(teta^2)*z; %raspunsul in accelaratii (m/s^2) h31=figure(3) plot(t,zpp) set(h31,'color',[0.908 0.648 0.41]) set(h31,'name','Masterand Maria Solonaru, RCSC, an I') h32=plot(t,zpp,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h32(1),'color',[1 0.43 0.23]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.231 0.54 0.4]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspunsul liber amortizat in acceleratii'); set(h33,'fontname','times','fontsize',16') set(h33,'color',[ 0.231 0.2 0.7]) h34=xlabel('timpul (t)'); set(h34,'fontname','times','fontsize',20) set(h34,'color',[ 0.865 0.9 0.5]) h35=ylabel('acceleratia m/s^2'); set(h35,'fontname','times','fontsize',18) set(h35,'color',[ 0.43 0.43 0.1]) set(gca,'color',[0.12 0.23 0.6]) %calculul minimului si maximului [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h36=text(t(imax)*0.8,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(zpp(imax))]) set(h36,'fontweight','bold') h37=text(t(imin)*0.8,0.95*zppmin,['minim=',num2str(zppmin),' pentru t=',num2str(zpp(imin))]) set(h37,'fontweight','bold') h41=figure(4) %grafic comparativ set(h41,'color',[0.98 0.432 0.3]) set(h41,'name','Masterand Maria Solonaru, RCSC, an I') subplot(3,1,1) plot(t,z) subplot(3,1,2) plot(t,zp) subplot(3,1,3)


Solonaru Maria

plot(t,zpp) V=m*zpp h51=figure(5) %Graficul fortei taietoare plot(t,V); set(h51,'color',[0 0.786 0.3]); set(h51,'name','Masterand Maria Solonaru, RCSC, an I'); h52=plot(t,V,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h52(1),'color',[0.54 0.6 0.243]); set(h52(1),'linewidth',[2]); set(h52(2),'color',[0.9 1 0.4]); set(h52(2),'linewidth',[2]); set(h52(2),'linestyle','--'); h53=title('Graficul fortei taietoare'); set(h53,'fontname','times','fontsize',16') set(h53,'color',[ 1 0.2 0.7]); h54=xlabel('timpul (t)'); set(h54,'fontname','times','fontsize',20) set(h54,'color',[ 0.64 0.78 0.1]); h55=ylabel('ft'); set(h55,'fontname','times','fontsize',18) set(h55,'color',[ 0.1 1 1]); set(gca,'color',[0.12435 0.23 0.6]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h56=text(t(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(V(imax))]) set(h56,'fontweight','bold') h57=text(t(imin)*1.10,0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(V(imin))]) set(h57,'fontweight','bold') M=V*h h61=figure(6) %Graficul momentului incovoietor plot(t,M); set(h61,'color',[0.6590 0.968 0.3]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(t,M,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h62(1),'color',[1 0.67 0.76]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.98 0.54 0.4]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul momentului incovoietor'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.23 0.98 0.3]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.234 0.789 0.1]); h65=ylabel('mi'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 1 0 0.54]); set(gca,'color',[0.37 0.8 0.6]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h66=text(t(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(M(imax))]) set(h66,'fontweight','bold') h67=text(t(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(M(imin))]) set(h67,'fontweight','bold')


Solonaru Maria

sigma =(M*hs)/(2*I) h71=figure(7) %Graficul efortului axial plot(t,sigma); set(h71,'color',[0.23 0.9 0.3]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(t,sigma,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h72(1),'color',[1 0.5 0.2]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0 0.54 0.4]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul efortului axial'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.6 0.2 0.7]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.1 0.78 0.1]); h75=ylabel('sigma'); set(h75,'fontname','times','fontsize',18) set(h75,'color',[ 0.78 0.2 0.1]); set(gca,'color',[0.43 0.78 0.6]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h76=text(t(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(sigma(imax))]) set(h76,'fontweight','bold') h77=text(t(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(sigma(imin))]) set(h77,'fontweight','bold') tau =(V*hs^2)/(8*I) h81=figure(8) %Graficul efortului tangential plot(t,tau); set(h81,'color',[0.99 0.88 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(t,tau,[0 t(end)],[0 0], '--',t,inf,t,-inf); set(h82(1),'color',[1 0.78 0.78]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.98 1 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului tangential'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.85 0.546 0.1]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.243 0.2 0.5]); h85=ylabel('tau'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.746 0.56 1]); set(gca,'color',[0.968 0 0.243]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h86=text(t(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(tau(imax))]) set(h86,'fontweight','bold') h87=text(t(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(tau(imin))]) set(h87,'fontweight','bold')

3. Rezultate


Solonaru Maria


Solonaru Maria

PROBLEMA NR. 7

Calculul unei structuri cu 1GDL folosind Teoria Sistemelor – varianta I1





seismului din Vrancea, 4 martie 1977, folosind Teoria Sistemelor


Conform Dinamicii Construcţiilor:

𝑚𝑧 + 𝑘𝑧 = 𝑓


𝑧 = −𝑘

𝑚𝑧 +

𝑓

𝑚

Conform Teoriei Sistemelor:

𝑥 = 𝐴𝑥 + 𝐵𝑓 𝑒𝑐𝑢𝑎ţ𝑖𝑎 𝑑𝑒 𝑠𝑡𝑎𝑟𝑒

𝑦 = 𝐶𝑥 + 𝐷𝑓 𝑒𝑐𝑢𝑎ţ𝑖𝑎 𝑑𝑒 𝑚ă𝑠𝑢𝑟𝑎𝑟𝑒

C= [I] ; D= [0]

𝑥 = 𝑧

𝑧


Solonaru Maria

𝑧

𝑧 = 𝐴

𝑧

𝑧 + 𝐵𝑓 =

𝐴11

𝐴21 𝐴12

𝐴22

𝑧

𝑧 +

𝐵1

𝐵2

𝑓

𝑧 = 𝐴11𝑧 + 𝐴12𝑧 + 𝐵1𝑓

𝑧 = 𝐴21𝑧 + 𝐴22𝑧 + 𝐵2𝑓

Rezultă:

𝐴 = 0

−𝑘𝑚

0

0

𝐵 = 01𝑚



%masterand Solonaru Maria, RCSC, an I close all clear all disp('Structuri cu 1GDL - Raspuns seismic liber neamortizat in Teoria Sistemelor') % date de intrare bs=20; %latimea sectiunii(cm) bs=bs/100; hs=40; %inaltimea sectiunii(cm) hs=hs/100; m=1e5; %masa structurii(kg) E=2.1e6; %modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii(m) %calculul caracteristicilor geometrice I=bs*hs^3/12; % momentul de inertie(m^4) % calculul caracteristicilor elastice delta=h^3/3/E/I; % flexibilitatea (m/N) k=1/delta; %rigiditatea (N/m) % calculul caracteristicilor dinamice omega =sqrt(k/m); %pulsatia (frecventa circulara)(rad/s) T=2*pi/omega; % perioada proprie de vibratie(s) f=1/T; % frecventa proprie(Hz) load VRAN.ACC [n,mc]=size(VRAN); pt=0.02 %pasul de timp timp=0:pt:(n-1)*pt, estvest=VRAN(:,1); nordsud=VRAN(:,2)/100; [y1max,i1max]=max(nordsud) [y1min,i1min]=min(nordsud) vertical=VRAN(:,3)/100; h11=figure(1) set(h11,'color',[1 1 0]) set(h11,'name','Seism Vrancea') h12=plot(timp,nordsud,[0 timp(end)],[0 0])


Solonaru Maria

set(h12(1),'color',[1 0.54 1]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.5 0.54 0.4]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') ax=axis; ax(2)=timp(end) ax(3)=y1min*1.1 ax(4)=y1max*1.1 axis(ax); set(gca,'color',[0.5 0.9 0.6]) %alcatuirea matricei A A=[ 0 1; -k/m 0]; [U,W]=eig(A); %verificare niu si omega rp=real(W(1,1)); ip=imag(W(1,1)); rap=rp/ip; vniu=abs(rap/sqrt(1+rap^2)); vomega=-rp/vniu; %alcatuirea matricei B B=[ 0; 1/m]; %alcatuirea matricei C C=[ 1 0; 0 1 -k/m 0]; %alcatuirea matricei D D=[ 0; 0 1/m ]; % crearea sistemului conform Teoriei Sistemelor s1gld=ss(A,B,C,D) %vectorul fortelor exterioare fext=m*nordsud'; %raspunsul seismic al sistemului creat y=lsim(s1gld,fext,timp); z=y(:,1); h21=figure(2); set(h21,'color',[0.98 1 0.3]) set(h21,'name','masterand Maria Solonaru, RCSC an I') h22=plot(timp,z,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h22(1),'color',[0.5 0.543 0]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.786 1 1]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspunsul seismic al structurii cu 1gdl'); set(h23,'fontname','times','fontsize',16') set(h23,'color',[ 0.6 0.2 0.7]) h24=xlabel('timpul (t)'); set(h24,'fontname','times','fontsize',20) set(h24,'color',[ 0.8 0.2 0.5]) h25=ylabel('deplasarea (m)'); set(h25,'fontname','times','fontsize',18) set(h25,'color',[ 0.7 0.5 0.1]) set(gca,'color',[0.987 0.23 0.6]) %calculul minimului si maximului [zmax,imax]=max(z);


Solonaru Maria

[zmin,imin]=min(z); h26=text(timp(imax)*0.9,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(z(imax))]) set(h26,'fontweight','bold') h27=text(timp(imin)*0.75,0.95*zmin,['minim=',num2str(zmin),' pentru t=',num2str(z(imin))]) set(h27,'fontweight','bold') zp=y(:,2); h31=figure(3); set(h31,'color',[0.6 0.2314 1]) set(h31,'name','masterand Maria Solonaru, RCSC an I') h32=plot(timp,zp,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h32(1),'color',[1 0.324 0.546]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.43 0.54 0.4]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspunsul seismic al structurii cu 1gdl'); set(h33,'fontname','times','fontsize',16') set(h33,'color',[ 0.907 0.2 0.7]) h34=xlabel('timpul (t)'); set(h34,'fontname','times','fontsize',20) set(h34,'color',[ 0.1 0.65 1]) h35=ylabel('viteza (s)'); set(h35,'fontname','times','fontsize',18) set(h35,'color',[ 1 0.78 0.1]) set(gca,'color',[1 0.56 0.6]) %calculul minimului si maximului [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h36=text(timp(imax)*0.8,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(timp(imax))]) set(h36,'fontweight','bold') h37=text(timp(imin)*0.8,0.95*zpmin,['minim=',num2str(zpmin),' pentru t=',num2str(timp(imin))]) set(h37,'fontweight','bold') zpp=y(:,3); h41=figure(4); set(h41,'color',[1 0.76 0.1]) set(h41,'name','masterand Maria Solonaru, RCSC an I') h42=plot(timp,zpp,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h42(1),'color',[0.1 0.54 1]) set(h42(1),'linewidth',[2]) set(h42(2),'color',[0.9 1 0.4]) set(h42(2),'linewidth',[2]) set(h42(2),'linestyle','--') h43=title('Raspunsul seismic al structurii cu 1gdl'); set(h43,'fontname','times','fontsize',16') set(h43,'color',[ 0.98 0.2 0.7]) h44=xlabel('timpul (t)'); set(h44,'fontname','times','fontsize',20) set(h44,'color',[ 0.231 0.67 0.5]) h45=ylabel('acceleratia (m/s2)'); set(h45,'fontname','times','fontsize',18) set(h45,'color',[ 0.98 1 0.1]) set(gca,'color',[0.78 0.78 0]) %calculul minimului si maximului [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h46=text(timp(imax)*0.8,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(timp(imax))]) set(h46,'fontweight','bold') h47=text(timp(imin)*0.8,0.95*zppmin,['minim=',num2str(zppmin),' pentru t=',num2str(timp(imin))]) set(h47,'fontweight','bold') h51=figure(5) %grafic comparativ


Solonaru Maria

set(h51,'color',[0.689 0.234 0.43]) set(h51,'name','Masterand Maria Solonaru, RCSC, an I') set(h51,'Position',[150 50 600 500]) subplot(4,1,2) plot(timp,z) subplot(4,1,3) plot(timp,zp) subplot(4,1,4) plot(timp,zpp) V=m*zpp h61=figure(6) %Graficul fortei taietoare plot(timp,V); set(h61,'color',[0.98 0.7 0.3]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(timp,V,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h62(1),'color',[0.54 0.65 0.65]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.78 0.2 0.4]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul fortei taietoare'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.2 0.2 0.7]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.98 0.43 0.1]); h65=ylabel('ft'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.785 0.54 0.1]); set(gca,'color',[0.2315 0.65 0.6]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h66=text(timp(imax)*0.8,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(timp(imax))]) set(h66,'fontweight','bold') h67=text(timp(imin)*0.8,0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(timp(imin))]) set(h67,'fontweight','bold') M=V*h h71=figure(7) %Graficul momentului incovoietor plot(timp,M); set(h71,'color',[0.11 0.7 0.3]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(timp,M,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h72(1),'color',[1 0.67 0.65]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.13 0.23 0.4]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul momentului incovoietor'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.98 0.3 0]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0 1 0.1]); h75=ylabel('mi'); set(h75,'fontname','times','fontsize',18) set(h75,'color',[ 0.1 0.98 0.1]); set(gca,'color',[0.978 0.8 0.6]); %calculul minimului si maximului [Mmax,imax]=max(M);


Solonaru Maria

[Mmin,imin]=min(M); h76=text(timp(imax)*0.8,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(timp(imax))]) set(h76,'fontweight','bold') h77=text(timp(imin)*0.8,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(timp(imin))]) set(h77,'fontweight','bold') sigma =(M*hs)/(2*I) h81=figure(8) %Graficul efortului axial plot(timp,sigma); set(h81,'color',[0.9 0.77 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(timp,sigma,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h82(1),'color',[0.8 0.78 0.4]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.2 1 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului axial'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.6 0.2 0.7]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.78 0.78 0.1]); h85=ylabel('sigma'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.2 0.98 0.1]); set(gca,'color',[0.54 1 0.6]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h86=text(timp(imax)*0.8,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(timp(imax))]) set(h86,'fontweight','bold') h87=text(timp(imin)*0.8,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(timp(imin))]) set(h87,'fontweight','bold') tau =(V*hs^2)/(8*I) h91=figure(9) %Graficul efortului tangential plot(timp,tau); set(h91,'color',[1 0.88 0.3]); set(h91,'name','Masterand Maria Solonaru, RCSC, an I'); h92=plot(timp,tau,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h92(1),'color',[1 0.78 0.98]); set(h92(1),'linewidth',[2]); set(h92(2),'color',[1 1 0.4]); set(h92(2),'linewidth',[2]); set(h92(2),'linestyle','--'); h93=title('Graficul efortului tangential'); set(h93,'fontname','times','fontsize',16') set(h93,'color',[ 0.12 0.98 0.1]); h94=xlabel('timpul (t)'); set(h94,'fontname','times','fontsize',20) set(h94,'color',[ 0.67 0.2 0.5]); h95=ylabel('tau'); set(h95,'fontname','times','fontsize',18) set(h95,'color',[ 0.78 0.98 0.1]); set(gca,'color',[0.2143 1 0.6]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h96=text(timp(imax)*0.9,0.95*taumax,['max=',num2str(taumax),'pt t=',num2str(timp(imax))]) set(h96,'fontweight','bold')


Solonaru Maria

h97=text(timp(imin)*0.9,0.95*taumin,['min=',num2str(taumin),'pt t=',num2str(timp(imin))]) set(h97,'fontweight','bold')

4. Rezultate


Solonaru Maria

Calculul unei structure cu 1GDL folosind Teoria Sistemelor – varianta I2


Solonaru Maria





seismului din Vrancea, 4 martie 1977, folosind Teoria Sistemelor


Conform Dinamicii Construcţiilor :

𝑚𝑧 𝑡 + 𝑐𝑧 𝑡 + 𝑘𝑧 𝑡 = 𝑓


𝑧 𝑡 = −𝑘

𝑚𝑧 −

𝑐

𝑚𝑧 𝑡 +

𝑓

𝑚

Conform Teoriei Sistemelor:

𝑥 = 𝐴𝑥 + 𝐵𝑓 𝑒𝑐𝑢𝑎ţ𝑖𝑎 𝑑𝑒 𝑠𝑡𝑎𝑟𝑒

𝑦 = 𝐶𝑥 + 𝐷𝑓 𝑒𝑐𝑢𝑎ţ𝑖𝑎 𝑑𝑒 𝑚ă𝑠𝑢𝑟𝑎𝑟𝑒

C= [I] ; D= [0]

𝑥 = 𝑧

𝑧

𝑧

𝑧 = 𝐴

𝑧

𝑧 + 𝐵𝑓 =

𝐴11

𝐴21 𝐴12

𝐴22

𝑧

𝑧 +

𝐵1

𝐵2

𝑓

𝑧 = 𝐴11𝑧 + 𝐴12𝑧 + 𝐵1𝑓

𝑧 = 𝐴21𝑧 + 𝐴22𝑧 + 𝐵2𝑓

Rezultă:

𝐴 = 0

−𝑘𝑚

0

−𝑐𝑚

𝐵 = 01𝑚


%masterand Solonaru Maria, RCSC, an I close all clear all disp('Structuri cu 1GDL - Raspuns seismic liber amortizat in Teoria Sistemelor')


Solonaru Maria

% date de intrare bs=20; %latimea sectiunii(cm) bs=bs/100; hs=40; %inaltimea sectiunii(cm) hs=hs/100; m=1e5; %masa structurii(kg) E=2.1e6; %modulul de elasticitate(daN/cm^2) E=E*1e5; niu=5; %procentul din amortizarea critica(%) niu=niu/100; h=4; %inaltimea grinzii(m) %calculul caracteristicilor geometrice I=bs*hs^3/12; % momentul de inertie(m^4) % calculul caracteristicilor elastice delta=h^3/3/E/I; % flexibilitatea (m/N) k=1/delta; %rigiditatea (N/m) % calculul caracteristicilor dinamice omega =sqrt(k/m); %pulsatia (frecventa circulara)(rad/s) T=2*pi/omega; % perioada proprie de vibratie(s) f=1/T; % frecventa proprie(Hz) omegab=omega/sqrt(1-niu^2); %pulsatia (frecventa circulara)in regim amortizat rad/s) Tb=T*sqrt(1-niu^2);% perioada proprie de vibratie in regim amortizat(s) load VRAN.ACC [n,mc]=size(VRAN); pt=0.02 %pasul de timp timp=0:pt:(n-1)*pt, estvest=VRAN(:,1); nordsud=VRAN(:,2)/100; [y1max,i1max]=max(nordsud) [y1min,i1min]=min(nordsud) vertical=VRAN(:,3)/100; h11=figure(1) set(h11,'color',[1 0 1]) set(h11,'name','Seism Vrancea') h12=plot(timp,nordsud,[0 timp(end)],[0 0]) set(h12(1),'color',[0.2 0.54 0.43]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.67 0.43 0.4]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') ax=axis; ax(2)=timp(end) ax(3)=y1min*1.1 ax(4)=y1max*1.1 axis(ax); set(gca,'color',[0.78 0.543 0.6]) %coeficientul de amortizare c=2*niu*omega*m; %alcatuirea matricei A A=[ 0 1; -k/m -c/m]; [U,W]=eig(A); %verificare niu si omega rp=real(W(1,1)); ip=imag(W(1,1)); rap=rp/ip; vniu=abs(rap/sqrt(1+rap^2)); vomega=-rp/vniu; %alcatuirea matricei B B=[ 0;


Solonaru Maria

1/m]; %alcatuirea matricei C C=[ 1 0; 0 1 -k/m -c/m]; %alcatuirea matricei D D=[ 0; 0 1/m ]; % crearea sistemului conform Teoriei Sistemelor s1gld=ss(A,B,C,D) %vectorul fortelor exterioare fext=m*nordsud'; %raspunsul seismic al sistemului creat y=lsim(s1gld,fext,timp); z=y(:,1); h21=figure(2); set(h21,'color',[0.98 0.23 0.3]) set(h21,'name','masterand Maria Solonaru, RCSC an I') h22=plot(timp,z,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h22(1),'color',[1 0.54 0.54]) set(h22(1),'linewidth',[2]) set(h22(2),'color',[0.78 1 0.4]) set(h22(2),'linewidth',[2]) set(h22(2),'linestyle','--') h23=title('Raspunsul seismic al structurii cu 1gdl'); set(h23,'fontname','times','fontsize',16') set(h23,'color',[ 0.2314 0.2 0.7]) h24=xlabel('timpul (t)'); set(h24,'fontname','times','fontsize',20) set(h24,'color',[ 0.56 0.2 0.5]) h25=ylabel('deplasarea (m)'); set(h25,'fontname','times','fontsize',18) set(h25,'color',[ 0.77 0.5 1]) set(gca,'color',[0.978 0.8 0.2]) %calculul minimului si maximului [zmax,imax]=max(z); [zmin,imin]=min(z); h26=text(timp(imax)*1.10,0.95*zmax,['max=',num2str(zmax),'pt t=',num2str(z(imax))]) set(h26,'fontweight','bold') h27=text(timp(imin)*1.10,0.95*zmin,['min=',num2str(zmin),'pt t=',num2str(z(imin))]) set(h27,'fontweight','bold') zp=y(:,2); h31=figure(3); set(h31,'color',[0.234 0.243 0.8]) set(h31,'name','masterand Maria Solonaru, RCSC an I') h32=plot(timp,zp,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h32(1),'color',[0.43 0.45 1]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.98 1 0.4]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspunsul seismic al structurii cu 1gdl'); set(h33,'fontname','times','fontsize',16') set(h33,'color',[ 0.6 0.2 0.7]) h34=xlabel('timpul (t)'); set(h34,'fontname','times','fontsize',20) set(h34,'color',[ 0.5 0.6 0.5]) h35=ylabel('viteza (s)'); set(h35,'fontname','times','fontsize',18)


Solonaru Maria

set(h35,'color',[ 0 0.78 0.1]) set(gca,'color',[1 0.54 0.658]) %calculul minimului si maximului [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h36=text(timp(imax)*1.10,0.95*zpmax,['max=',num2str(zpmax),'pt t=',num2str(timp(imax))]) set(h36,'fontweight','bold') h37=text(timp(imin)*1.10,0.95*zpmin,['min=',num2str(zpmin),'pt t=',num2str(timp(imin))]) set(h37,'fontweight','bold') zpp=y(:,3); h41=figure(4); set(h41,'color',[0.78 0.54 0.243]) set(h41,'name','masterand Maria Solonaru, RCSC an I') h42=plot(timp,zpp,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h42(1),'color',[0.243 0.54 1]) set(h42(1),'linewidth',[2]) set(h42(2),'color',[0.67 0.1 0.4]) set(h42(2),'linewidth',[2]) set(h42(2),'linestyle','--') h43=title('Raspunsul seismic al structurii cu 1gdl'); set(h43,'fontname','times','fontsize',16') set(h43,'color',[ 0.3 0.2 0.7]) h44=xlabel('timpul (t)'); set(h44,'fontname','times','fontsize',20) set(h44,'color',[ 0.9 0.6 0.5]) h45=ylabel('acceleratia (m/s2)'); set(h45,'fontname','times','fontsize',18) set(h45,'color',[ 0.23 0.5462 0.1]) set(gca,'color',[0.2 0.67 1]) %calculul minimului si maximului [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h46=text(timp(imax)*1.10,0.95*zppmax,['max=',num2str(zppmax),'pt t=',num2str(timp(imax))]) set(h46,'fontweight','bold') h47=text(timp(imin)*1.10,0.95*zppmin,['min=',num2str(zppmin),'pt t=',num2str(timp(imin))]) set(h47,'fontweight','bold') h51=figure(5) %grafic comparativ set(h51,'color',[0.90 0.7 0.3]) set(h51,'name','Masterand Maria Solonaru, RCSC, an I') set(h51,'Position',[150 50 600 500]) subplot(4,1,2) plot(timp,z) subplot(4,1,3) plot(timp,zp) subplot(4,1,4) plot(timp,zpp) V=m*zpp h61=figure(6) %Graficul fortei taietoare plot(timp,V); set(h61,'color',[0.33 0.7 0.3]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(timp,V,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h62(1),'color',[0.43 0.54 0]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.98 1 0.4]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul fortei taietoare'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.67 0.2 0.7]);


Solonaru Maria

h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.8 0.11 0.87]); h65=ylabel('ft'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0 0.78 0.1]); set(gca,'color',[1 0.8 0]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h66=text(timp(imax)*1.10,0.95*Vmax,['max=',num2str(Vmax),'pt t=',num2str(timp(imax))]) set(h66,'fontweight','bold') h67=text(timp(imin+300),0.95*Vmin,['min=',num2str(Vmin),'pt t=',num2str(timp(imin))]) set(h67,'fontweight','bold') M=V*h h71=figure(7) %Graficul momentului incovoietor plot(timp,M); set(h71,'color',[0.11 0.7 0.3]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(timp,M,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h72(1),'color',[0.23 0.6 0]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.8 1 0.4]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul momentului incovoietor'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0 0.3 0.3]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.1 0 0.1]); h75=ylabel('mi'); set(h75,'fontname','times','fontsize',18) set(h75,'color',[ 0.5 0.9 0.1]); set(gca,'color',[0.7 0.1 0.2]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h76=text(timp(imax)*1.10,0.95*Mmax,['max=',num2str(Mmax),'pt t=',num2str(timp(imax))]) set(h76,'fontweight','bold') h77=text(timp(imin)*1.10,0.95*Mmin,['min=',num2str(Mmin),'pt t=',num2str(timp(imin))]) set(h77,'fontweight','bold') sigma =(M*hs)/(2*I) h81=figure(8) %Graficul efortului axial plot(timp,sigma); set(h81,'color',[0.3 0.77 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(timp,sigma,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h82(1),'color',[1 0.6 0]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.9 0 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului axial'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.6 0.2 0.7]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.1 0.89 0.43]); h85=ylabel('sigma');


Solonaru Maria

set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.23 0.23 0.1]); set(gca,'color',[0.98 0.8 0.6]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h86=text(timp(imax)*1.10,0.95*sigmamax,['max=',num2str(sigmamax),'pt t=',num2str(timp(imax))]) set(h86,'fontweight','bold') h87=text(timp(imin)*1.10,0.95*sigmamin,['min=',num2str(sigmamin),'pt t=',num2str(timp(imin))]) set(h87,'fontweight','bold') tau =(V*hs^2)/(8*I) h91=figure(9) %Graficul efortului tangential plot(timp,tau); set(h91,'color',[0 0.2 0.3]); set(h91,'name','Masterand Maria Solonaru, RCSC, an I'); h92=plot(timp,tau,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h92(1),'color',[1 0.54 0]); set(h92(1),'linewidth',[2]); set(h92(2),'color',[0.7 0 0.4]); set(h92(2),'linewidth',[2]); set(h92(2),'linestyle','--'); h93=title('Graficul efortului tangential'); set(h93,'fontname','times','fontsize',16') set(h93,'color',[ 0.2 0.21 0.9]); h94=xlabel('timpul (t)'); set(h94,'fontname','times','fontsize',20) set(h94,'color',[ 0.8 0.2 0.5]); h95=ylabel('tau'); set(h95,'fontname','times','fontsize',18) set(h95,'color',[ 1 0.54 0.1]); set(gca,'color',[0.8 0.1 0.6]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h96=text(timp(imax)*1.10,0.95*taumax,['max=',num2str(taumax),'pt t=',num2str(timp(imax))]) set(h96,'fontweight','bold') h97=text(timp(imin)*1.10,0.95*taumin,['min=',num2str(taumin),'pt t=',num2str(timp(imin))]) set(h97,'fontweight','bold')

4. Rezultate


Solonaru Maria


Solonaru Maria

Calculul unei structuri cu 1GDL folosind Teoria Sistemelor – varianta II1


% masterand Maria Solonaru, RCSC, an I close all clear all disp('structuri cu 1GDL - raspuns la impuls in regim neamortizat liber- teoria sistemelor') % date de intrare bs=20; %latimea sectiunii bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) %calculul caracteristicilor geometrice %momentul de inertie (m^4) I=bs*hs^3/12; %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamice omega=sqrt(k/m); %pulsatia (rad/s) T=2*pi/omega; %perioada proprie de vibratia(s) f=1/T; % frecventa proprie (Hz) % alcatuirea vectorului timp nt=1000; pt=0.01;% pasul de timp timp=0:pt:(nt-1)*pt; % alcatuirea matricei A A=[ 0 1; -k/m 0] [U,W]=eig(A);


Solonaru Maria

% verificare omega rp=real(W(1,1)); ip=imag(W(1,1)); rap=rp/ip; vniu=abs(rap/sqrt(1+rap^2)); vomega=-rp/vniu; % alcatuirea matricei B B=[ 0; 1/m]; % alcatuirea matricei C C=[ 1 0; 0 1; -k/m 0]; % alcatuirea matricei D D=[ 0; 0; 1/m]; % crearea sistemului conform teoriei sistemelor s1gld=ss(A,B,C,D) % raspunsul la impuls in regim liber neamortizat al sistemului creat y=impulse(s1gld,timp); z=y(:,1); h11=figure(1); set(h11,'name','masterand Solonaru Maria - RCSC an I') set(h11,'color',[0.1 1 0.8]) h12=plot(timp,z,[0 timp(end)],[0 0]) set(gca,'color',[0.78 0.243 0.8]) set(h12(1),'color',[1 0.243 0.43]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0.78 0.24 0.5]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('Raspuns liber neamortizat la impuls'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[0 0.78 1]) h14=xlabel('timpul (s)'); set(h14,'fontname','times','fontsize',16) set(h14,'color',[0.8 1 0.6]) h15=ylabel('deplasarea (m)'); set(h15,'fontname','times','fontsize',16) set(h15,'color',[0.98 0.243 0.8]) set(gca,'color',[0.124 0.6 0.8]) %calc max si min [zmax,imax]=max(z); [zmin,imin]=min(z); h16=text(timp(imax)*1.10,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(timp(imax))]) set(h16,'fontweight','bold') h17=text(timp(imin),0.95*zmin,['minim=',num2str(zmin),'pentru t=',num2str(timp(imin))]) set(h17,'fontweight','bold') set(h11,'Position',[150 50 600 500]) zp=y(:,2); h31=figure(2); set(h31,'name','masterand Solonaru Maria - RCSC an I') set(h31,'color',[0.243 0 0.8]) h32=plot(timp,zp,[0 timp(end)],[0 0]) set(gca,'color',[0.907 0.43 0.8]) set(h32(1),'color',[0.43 0.43 0.43]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0 0.43 0.5]) set(h32(2),'linewidth',[2])


Solonaru Maria

set(h32(2),'linestyle','--') h33=title('Raspuns liber neamortizat la impuls'); set(h33,'fontname','times','fontsize',18) set(h33,'color',[0.43 0.5 1]) h34=xlabel('timpul (s)'); set(h34,'fontname','times','fontsize',16) set(h34,'color',[0.78 1 0.6]) h35=ylabel('viteza (s)'); set(h35,'fontname','times','fontsize',16) set(h35,'color',[0.978 0.98 0.1]) set(gca,'color',[0.23 0.67 0.8]) %calc max si min [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h36=text(timp(imax)*1.10,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(timp(imax))]) set(h36,'fontweight','bold') h37=text(timp(imin),0.95*zpmin,['minim=',num2str(zpmin),'pentru t=',num2str(timp(imin))]) set(h37,'fontweight','bold') set(h31,'Position',[150 50 600 500]) zpp=y(:,3); h41=figure(3); set(h41,'name','masterand Solonaru Maria - RCSC an I') set(h41,'color',[0.8 0 1]) h42=plot(timp,zpp,[0 timp(end)],[0 0]) set(gca,'color',[0.1 0.43 0.8]) set(h42(1),'color',[1 0.452 0.43]) set(h42(1),'linewidth',[2]) set(h42(2),'color',[0.432 0.23 0.5]) set(h42(2),'linewidth',[2]) set(h42(2),'linestyle','--') h43=title('Raspuns liber neamortizat la impuls'); set(h43,'fontname','times','fontsize',18) set(h43,'color',[0.65 0.785 1]) h44=xlabel('timpul (s)'); set(h44,'fontname','times','fontsize',16) set(h44,'color',[0.9968 1 0.98]) h45=ylabel('acceleratia(m/s2)'); set(h45,'fontname','times','fontsize',16) set(h45,'color',[0.234 0.54 0.8]) set(gca,'color',[0.98 0.1 0.8]) %calc max si min [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h46=text(timp(imax)*1.10,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(timp(imax))]) set(h46,'fontweight','bold') h47=text(timp(imin)*1,0.95*zppmin,['minim=',num2str(zppmin),'pentru t=',num2str(timp(imin))]) set(h47,'fontweight','bold') set(h41,'Position',[150 50 600 500]) h51=figure(4) %grafic comparativ set(h51,'color',[0.8 0.1 0.3]) set(h51,'name','Masterand Maria Solonaru, RCSC, an I') set(h51,'Position',[150 50 600 500]) subplot(4,1,2) plot(timp,z) subplot(4,1,3) plot(timp,zp) subplot(4,1,4) plot(timp,zpp) V=m*zpp h61=figure(5) %Graficul fortei taietoare


Solonaru Maria

plot(timp,V); set(h61,'color',[0.33 0.7 0.3]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(timp,V,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h62(1),'color',[1 0.78 0.67]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.98 1 0.4]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul fortei taietoare'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0.23 0.2 0.7]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 0.78 0.67 0.1]); h65=ylabel('ft'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.1 0.78 0.1]); set(gca,'color',[0.2 0.231 0.6]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h66=text(timp(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(timp(imax))]) set(h66,'fontweight','bold') h67=text(timp(imin),0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(timp(imin))]) set(h67,'fontweight','bold') M=V*h h71=figure(6) %Graficul momentului incovoietor plot(timp,M); set(h71,'color',[0.11 0.65 0.3]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(timp,M,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h72(1),'color',[1 0.78 0]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.52 1 0.4]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul momentului incovoietor'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.3 0.98 0.3]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.3 0.98 0.1]); h75=ylabel('mi'); set(h75,'fontname','times','fontsize',18) set(h75,'color',[ 0.2 0.978 0.9]); set(gca,'color',[0.2 0.78 0.6]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h76=text(timp(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(timp(imax))]) set(h76,'fontweight','bold') h77=text(timp(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(timp(imin))]) set(h77,'fontweight','bold') sigma =(M*hs)/(2*I) h81=figure(7) %Graficul efortului axial plot(timp,sigma); set(h81,'color',[0.0 0.723 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(timp,sigma,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf);


Solonaru Maria

set(h82(1),'color',[1 0.67 0.2]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.1 1 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului axial'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.45 0.2 0.7]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.98 0.1 0.1]); h85=ylabel('sigma'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 1 0.54 0.1]); set(gca,'color',[1 0.8 0.6]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h86=text(timp(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(timp(imax))]) set(h86,'fontweight','bold') h87=text(timp(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(timp(imin))]) set(h87,'fontweight','bold') tau =(V*hs^2)/(8*I) h91=figure(8) %Graficul efortului tangential plot(timp,tau); set(h91,'color',[0 0.88 1]); set(h91,'name','Masterand Maria Solonaru, RCSC, an I'); h92=plot(timp,tau,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h92(1),'color',[0.54 0.54 0]); set(h92(1),'linewidth',[2]); set(h92(2),'color',[0.7 0.1 0.4]); set(h92(2),'linewidth',[2]); set(h92(2),'linestyle','--'); h93=title('Graficul efortului tangential'); set(h93,'fontname','times','fontsize',16') set(h93,'color',[ 0.354 0.78 0.1]); h94=xlabel('timpul (t)'); set(h94,'fontname','times','fontsize',20) set(h94,'color',[ 0.8 0.78 0.5]); h95=ylabel('tau'); set(h95,'fontname','times','fontsize',18) set(h95,'color',[ 0.1 0 0.1]); set(gca,'color',[0.4 1 0.6]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h96=text(timp(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(timp(imax))]) set(h96,'fontweight','bold') h97=text(timp(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(timp(imin))]) set(h97,'fontweight','bold')

2. Rezultate


Solonaru Maria


Solonaru Maria

Calculul unei structuri cu 1GDL folosind Teoria Sistemelor – varianta II2


% masterand Maria Solonaru, RCSC, an I close all clear all disp('structuri cu 1GDL - raspuns la impuls in regim amortizat liber- teoria sistemelor') % date de intrare bs=20; %latimea sectiunii bs=bs/100; hs=40; %inaltimea sectiunii (cm) hs=hs/100; m=1e5; %masa (kg) niu=5; %procentul din amortizarea critica (%) niu=niu/100; E=2.1e6;%modulul de elasticitate(daN/cm^2) E=E*1e5; h=4; %inaltimea grinzii (m) %calculul caracteristicilor geometrice %momentul de inertie (m^4) I=bs*hs^3/12; %calculul caracteristicilor elastice %flexibilitatea (m/N) delta=h^3/3/E/I; %rigiditatea (N/m) k=1/delta; %calculul caracteristicilor dinamice omega=sqrt(k/m); %pulsatia (rad/s) T=2*pi/omega; %perioada proprie de vibratia(s) f=1/T; % frecventa proprie (Hz) omegab=omega/sqrt(1-niu^2); %pulsatia in regim amortizzat Tb=T*sqrt(1-niu^2); % perioada de vibratie in reg amortizat fb=1/Tb; % alcatuirea vectorului timp nt=1000; pt=0.01;% pasul de timp timp=0:pt:(nt-1)*pt;


Solonaru Maria

% coeficientul de amortizare c=2*niu*omega*m; % alcatuirea matricei A A=[ 0 1; -k/m -c/m] [U,W]=eig(A); % verificare niu si omega rp=real(W(1,1)); ip=imag(W(1,1)); rap=rp/ip; vniu=abs(rap/sqrt(1+rap^2)); vomega=-rp/vniu; % alcatuirea matricei B B=[ 0; 1/m]; % alcatuirea matricei C C=[ 1 0; 0 1; -k/m -c/m]; % alcatuirea matricei D D=[ 0; 0; 1/m]; % crearea sistemului conform teoriei sistemelor s1gld=ss(A,B,C,D) % raspunsul la impuls al sistemului creat y=impulse(s1gld,timp); z=y(:,1); h11=figure(1); set(h11,'name','masterand Solonaru Maria - RCSC an I') set(h11,'color',[0.78 1 0.8]) h12=plot(timp,z,[0 timp(end)],[0 0]) set(gca,'color',[1 0.9 0.8]) set(h12(1),'color',[1 0.542 0]) set(h12(1),'linewidth',[2]) set(h12(2),'color',[0 0.9 0.5]) set(h12(2),'linewidth',[2]) set(h12(2),'linestyle','--') h13=title('Raspuns liber amortizat la impuls'); set(h13,'fontname','times','fontsize',18) set(h13,'color',[1 0.978 1]) h14=xlabel('timpul (s)'); set(h14,'fontname','times','fontsize',16) set(h14,'color',[0.432 1 0.6]) h15=ylabel('deplasarea (m)'); set(h15,'fontname','times','fontsize',16) set(h15,'color',[0.3 0.6 0.8]) set(gca,'color',[0.98 0.92 0.8]) %calc max si min [zmax,imax]=max(z); [zmin,imin]=min(z); h16=text(timp(imax)*1.10,0.95*zmax,['maxim=',num2str(zmax),' pentru t=',num2str(timp(imax))]) set(h16,'fontweight','bold') h17=text(timp(imin+300),0.95*zmin,['minim=',num2str(zmin),'pentru t=',num2str(timp(imin))]) set(h17,'fontweight','bold') set(h11,'Position',[150 50 600 500]) zp=y(:,2); h31=figure(2); set(h31,'name','masterand Solonaru Maria - RCSC an I') set(h31,'color',[0 1 0.8])


Solonaru Maria

h32=plot(timp,zp,[0 timp(end)],[0 0]) set(gca,'color',[0.2 0 0.8]) set(h32(1),'color',[1 0.65 0.67]) set(h32(1),'linewidth',[2]) set(h32(2),'color',[0.9 0.243 0.5]) set(h32(2),'linewidth',[2]) set(h32(2),'linestyle','--') h33=title('Raspuns liber amortizat la impuls'); set(h33,'fontname','times','fontsize',18) set(h33,'color',[1 0.234 0]) h34=xlabel('timpul (s)'); set(h34,'fontname','times','fontsize',16) set(h34,'color',[0.243 0 0.6]) h35=ylabel('viteza (s)'); set(h35,'fontname','times','fontsize',16) set(h35,'color',[0.231 0.6 1]) set(gca,'color',[0.231 0.9 0.8]) %calc max si min [zpmax,imax]=max(zp); [zpmin,imin]=min(zp); h36=text(timp(imax)*1.10,0.95*zpmax,['maxim=',num2str(zpmax),' pentru t=',num2str(timp(imax))]) set(h36,'fontweight','bold') h37=text(timp(imin+300),0.95*zpmin,['minim=',num2str(zpmin),'pentru t=',num2str(timp(imin))]) set(h37,'fontweight','bold') set(h31,'Position',[150 50 600 500]) zpp=y(:,3); h41=figure(3); set(h41,'name','masterand Solonaru Maria - RCSC an I') set(h41,'color',[0.8 0.4 0.8]) h42=plot(timp,zpp,[0 timp(end)],[0 0]) set(gca,'color',[0.59 0 0.8]) set(h42(1),'color',[1 0.756 0.65]) set(h42(1),'linewidth',[2]) set(h42(2),'color',[0.3 0.6 0.5]) set(h42(2),'linewidth',[2]) set(h42(2),'linestyle','--') h43=title('Raspuns liber amortizat la impuls'); set(h43,'fontname','times','fontsize',18) set(h43,'color',[0.223 0.43 1]) h44=xlabel('timpul (s)'); set(h44,'fontname','times','fontsize',16) set(h44,'color',[0.2 0 0.6]) h45=ylabel('acceleratia(m/s2)'); set(h45,'fontname','times','fontsize',16) set(h45,'color',[0.231 0.6 0.8]) set(gca,'color',[0.9 0.2 0.8]) %calc max si min [zppmax,imax]=max(zpp); [zppmin,imin]=min(zpp); h46=text(timp(imax)*1.10,0.95*zppmax,['maxim=',num2str(zppmax),' pentru t=',num2str(timp(imax))]) set(h46,'fontweight','bold') h47=text(timp(imin+300),0.95*zppmin,['minim=',num2str(zppmin),'pentru t=',num2str(timp(imin))]) set(h47,'fontweight','bold') set(h41,'Position',[150 50 600 500]) h51=figure(4) %grafic comparativ set(h51,'color',[0.1 0.53 0.3]) set(h51,'name','Masterand Maria Solonaru, RCSC, an I') set(h51,'Position',[150 50 600 500]) subplot(4,1,2) plot(timp,z)


Solonaru Maria

subplot(4,1,3) plot(timp,zp) subplot(4,1,4) plot(timp,zpp) V=m*zpp h61=figure(5) %Graficul fortei taietoare plot(timp,V); set(h61,'color',[0.33 0.7 0.3]); set(h61,'name','Masterand Maria Solonaru, RCSC, an I'); h62=plot(timp,V,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h62(1),'color',[1 0.67 0.67]); set(h62(1),'linewidth',[2]); set(h62(2),'color',[0.98 1 0.4]); set(h62(2),'linewidth',[2]); set(h62(2),'linestyle','--'); h63=title('Graficul fortei taietoare'); set(h63,'fontname','times','fontsize',16') set(h63,'color',[ 0 0.2 0.7]); h64=xlabel('timpul (t)'); set(h64,'fontname','times','fontsize',20) set(h64,'color',[ 1 0.67 0.1]); h65=ylabel('ft'); set(h65,'fontname','times','fontsize',18) set(h65,'color',[ 0.1 0.1 0.1]); set(gca,'color',[0.9 0.8 0.6]); %calculul minimului si maximului [Vmax,imax]=max(V); [Vmin,imin]=min(V); h66=text(timp(imax)*1.10,0.95*Vmax,['maxim=',num2str(Vmax),' pentru t=',num2str(timp(imax))]) set(h66,'fontweight','bold') h67=text(timp(imin+300),0.95*Vmin,['minim=',num2str(Vmin),' pentru t=',num2str(timp(imin))]) set(h67,'fontweight','bold') M=V*h h71=figure(6) %Graficul momentului incovoietor plot(timp,M); set(h71,'color',[0.2 0.7 0.3]); set(h71,'name','Masterand Maria Solonaru, RCSC, an I'); h72=plot(timp,M,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h72(1),'color',[1 0 0]); set(h72(1),'linewidth',[2]); set(h72(2),'color',[0.5 0.3 0.4]); set(h72(2),'linewidth',[2]); set(h72(2),'linestyle','--'); h73=title('Graficul momentului incovoietor'); set(h73,'fontname','times','fontsize',16') set(h73,'color',[ 0.3 0.67 0.3]); h74=xlabel('timpul (t)'); set(h74,'fontname','times','fontsize',20) set(h74,'color',[ 0.1 0.1 0.1]); h75=ylabel('mi'); set(h75,'fontname','times','fontsize',18) set(h75,'color',[ 0.613 0.234 0.1]); set(gca,'color',[0.4 0.90 0.6]); %calculul minimului si maximului [Mmax,imax]=max(M); [Mmin,imin]=min(M); h76=text(timp(imax)*1.10,0.95*Mmax,['maxim=',num2str(Mmax),' pentru t=',num2str(timp(imax))]) set(h76,'fontweight','bold') h77=text(timp(imin)*1.10,0.95*Mmin,['minim=',num2str(Mmin),' pentru t=',num2str(timp(imin))]) set(h77,'fontweight','bold')


Solonaru Maria

sigma =(M*hs)/(2*I) h81=figure(7) %Graficul efortului axial plot(timp,sigma); set(h81,'color',[0.9 0.77 0.3]); set(h81,'name','Masterand Maria Solonaru, RCSC, an I'); h82=plot(timp,sigma,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h82(1),'color',[1 0.65 0]); set(h82(1),'linewidth',[2]); set(h82(2),'color',[0.432 0 0.4]); set(h82(2),'linewidth',[2]); set(h82(2),'linestyle','--'); h83=title('Graficul efortului axial'); set(h83,'fontname','times','fontsize',16') set(h83,'color',[ 0.231 0.2 0.7]); h84=xlabel('timpul (t)'); set(h84,'fontname','times','fontsize',20) set(h84,'color',[ 0.1 0.9 0.1]); h85=ylabel('sigma'); set(h85,'fontname','times','fontsize',18) set(h85,'color',[ 0.1 0.1 0.1]); set(gca,'color',[0.9 1 0.6]); %calculul minimului si maximului [sigmamax,imax]=max(sigma); [sigmamin,imin]=min(sigma); h86=text(timp(imax)*1.10,0.95*sigmamax,['maxim=',num2str(sigmamax),' pentru t=',num2str(timp(imax))]) set(h86,'fontweight','bold') h87=text(timp(imin)*1.10,0.95*sigmamin,['minim=',num2str(sigmamin),' pentru t=',num2str(timp(imin))]) set(h87,'fontweight','bold') tau =(V*hs^2)/(8*I) h91=figure(8) %Graficul efortului tangential plot(timp,tau); set(h91,'color',[0 0.4 0.3]); set(h91,'name','Masterand Maria Solonaru, RCSC, an I'); h92=plot(timp,tau,[0 timp(end)],[0 0], '--',timp,inf,timp,-inf); set(h92(1),'color',[0.243 0.54 0]); set(h92(1),'linewidth',[2]); set(h92(2),'color',[0.5 1 0.4]); set(h92(2),'linewidth',[2]); set(h92(2),'linestyle','--'); h93=title('Graficul efortului tangential'); set(h93,'fontname','times','fontsize',16') set(h93,'color',[ 0.78 0.1 0.1]); h94=xlabel('timpul (t)'); set(h94,'fontname','times','fontsize',20) set(h94,'color',[ 0.8 0.67 0.5]); h95=ylabel('tau'); set(h95,'fontname','times','fontsize',18) set(h95,'color',[ 0.231 0.5324 0.1]); set(gca,'color',[0.42 0.2 0.6]); %calculul minimului si maximului [taumax,imax]=max(tau); [taumin,imin]=min(tau); h96=text(timp(imax)*1.10,0.95*taumax,['maxim=',num2str(taumax),' pentru t=',num2str(timp(imax))]) set(h96,'fontweight','bold') h97=text(timp(imin)*1.10,0.95*taumin,['minim=',num2str(taumin),' pentru t=',num2str(timp(imin))]) set(h97,'fontweight','bold')


Solonaru Maria

2. Rezultate


Solonaru Maria

matlab

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