Analisis de vibraciones sistemas

Instituto Tecnológico de Saltillo

Ing. Mecatrónica

Programas en Matlab y Graficas de Sistemas Amortiguado Subamortiguado y Sobreamortiguado













Análisis de Vibraciones

Mario Arturo Mancilla Gutiérrez
08051334
Mecatrónica 7° Semestre
28– Noviembre- 2011

Programa 1
A=1;
w=pi;
tau=2;
for i=1:101
t(i)=tau*(i-1)/100;
x(i)=A*t(i)/tau;end
subplot(231);
plot(t,x,'r');
ylabel('x(t)');
xlabel('Tiempo');
title('x(t)=A*t/tau');
for i=1:101
x1(i)=A/2;
end
subplot(232);
plot(t,x1,'r');
xlabel('Tiempo');
title('Aprox N°1');
for i=1:101
x2(i)=A/2-A*sin(w*t(i))/pi-A*sin(2*w*t(i))/(2*pi)-A*sin(3*w*t(i))/(3*pi);
end
subplot(233);
plot(t,x2,'r');
xlabel('Tiempo');
title('Aprox N° 2');
for i=1:101x3(i)=A/2-A*sin(w*t(i))/pi-A*sin(2*w*t(i))/(2*pi)-A*sin(3*w*t(i))/(3*pi)-A*sin(4*w*t(i))/(4*pi);
end
subplot(234);
plot(t,x3,'r');
ylabel('x(t)');
xlabel('Tiempo');
title('Aprox N° 3');
for i=1:101
t(i)=tau*(i-1)/100;
x4(i)=A/2-A*sin(w*t(i))/pi-A*sin(2*w*t(i))/(2*pi)-A*sin(3*w*t(i))/(3*pi)-A*sin(4*w*t(i))/(4*pi)-A*sin(5*w*t(i))/(5*pi);
end
subplot(235);
plot(t,x4,'r');xlabel('Tiempo');
title('Aprox N°4');

Gráficas

Programa 2

%following 7 lines contain problem-dependent data
m=500.0;
k=36481.2;
c=1500.0;
x0=0.689865;
xd0=1.0;
n=200;
delt=0.030;
%end of problem-dependent data
[x,xd,xdd,t,ii]=frevib(m,k,c,x0,xd0,n,delt);
fprintf('Free vibration analysis \n');
fprintf('of a single degree of freedom analysis \n\n');
fprintf('Data:\n\n');
fprintf('m=%8.8e \n',m);
fprintf('k= %8.8e \n',k);
fprintf('c= %8.8e \n',c);
fprintf('x0= %8.8e \n',x0);
fprintf('xd0= %8.8e \n',xd0);
fprintf('n= %2.0f \n',n);
fprintf('delt= %8.8e \n\n\n',delt);
if ii==1
fprintf('system is undamped \n\n');
elseif ii==2
fprintf('system is under damped \n\n');
elseif ii==3
fprintf('system is critically damped \n\n');
elsefprintf('system is over damped \n\n');
end
fprintf('Result:\n\n');
fprintf(' i time(i) x(i) xd(i) xdd(i)');
fprintf('\n\n');
for i=1:100
fprintf('%2.0f %8.6e %8.6e %8.6e %8.6e \n',i,t(i),x(i),xd(i),xdd(i));
end
plot(t,x,'--r');
hold on;%almacenamiento de datos
gtext('x(t)');
plot(t,xd,'--b');
gtext('xd(t)');
plot(t,xdd,'--g');
gtext('xdd(t)');xlabel('TIEMPO');
ylabel('x(t), xd(t), xdd(t)');
title('Programa 2');

SUBRUTINA

function [x,xd,xdd,t,ii]=frevib(m,k,c,x0,xd0,n,delt);
omn=sqrt(k/m);
%subamortiguado sistema
if (abs(c)>1.0e-6)
ccrit=2.0*sqrt(k*m);
xai=c/ccrit;
if xai<1.0
%sobreamortiguado sistema
ii=2;
omd=sqrt(1.0-(xai^2))*omn;
cp1=x0;
cp2=(xd0+xai*omn*x0)/omd;a=sqrt(cp1^2+cp2^2);
phi=atan(cp1/cp2);
for i=1:n
if i>1
t(i)=t(i-1)+delt;
else
t(i)=delt;
end
tt=t(i);
x(i)=a*exp(-xai*omn*tt)*sin(omd*tt+phi);
xd(i)=a*exp(-xai*omn*tt)*(omd*cos(omd*tt+phi)-xai*omn*sin(omd*tt+phi));
xdd(i)=-(c*xd(i)+k*x(i))/m;end
elseif xai==1.0
%criticamente amortiguado sistema
ii=3;
for i=1:n
if i>1
t(i)=t(i-1)+delt;
else
t(i)=delt;
end
tt=t(i);
x(i)=(x0+(xd0+omn*x0)*tt)*exp(-omn*tt);
xd(i)=-(x0+(xd0*omn*x0)*tt)*omn*exp(-omn*tt)+(xd0+omn*x0)*exp(-omn*tt);xdd(i)=-(c*xd(i)+k*x(i))/m;
end
elseif xai>0
%overdamped system
ii=4;
x1=sqrt(xai^2-1,0);
c1=(x0*omn(xai+x1)+xd0)/(2.0*omn*x1);
c2=(-x0*omn(xai-x1)-xd0)/(2.0*omn*x1);
for i=1:n
if i>1
t(i)=t(i-1)+delt;
else
t(i)=delt;
end
tt=t(i);...