基于matlab实现的弹簧振动系统模型程序（动态模型）

news2025/10/31 6:34:05

完整代码：

clear all;

%System data
m=1.0; zeta=0.01; omega0=1.0; Dt=1.0; f0=1.0;
x0=0.0; dotx0=0.0;
xmax=sqrt(x0^2+(dotx0/omega0)^2)+min([0.5*abs(f0)*Dt/(m*omega0) f0/omega0^2]);
omegad=omega0*sqrt(1-zeta^2);
dt0=0.1*pi/omega0; nstep=500;

a=0.70; b=0.70; r=0.35*a; fact=0.50/xmax;

xf0=0.5*[0 -a 0 a 0]';
yf0=[0 -b/4 -b/2 -3*b/4 -b]';
xd1=0.5*[-a -a a a]';
yd1=[-6*b 0 0 -6*b]';
xd2=0.5*[-0.8*a 0.8*a]';
yd2=[-3*b -3*b]';
xf0=[xf0
xf0
xf0
xf0
xf0
xf0];
yf0=[yf0
-b+yf0
-2*b+yf0
-3*b+yf0
-4*b+yf0
-5*b+yf0];
xf=[0
xf0
0];
xSQ=[-a 5*a 5*a -a -a]';
ySQ=[0 0 -2*r -2*r 0]';
xH=[-2000 2000]'; yH=[0 0]';

xx=x0;
tt=0;

set(gcf,'DoubleBuffer','on');

i=1;
t=i*dt0;
t0=min([t Dt]);
t1=t-t0;
h=exp(-zeta*omega0*t)*sin(omegad*t)/(m*omegad);
doth=exp(-zeta*omega0*t)*(cos(omegad*t)-zeta*omega0/omegad*sin(omegad*t))/m;
H=(1/m-doth-2*zeta*omega0*h)/omega0^2;
h1=exp(-zeta*omega0*t1)*sin(omegad*t1)/(m*omegad);
doth1=exp(-zeta*omega0*t1)*(cos(omegad*t1)-zeta*omega0/omegad*sin(omegad*t1))/m;
H1=(1/m-doth1-2*zeta*omega0*h1)/omega0^2;
if t>Dt
t2=t-Dt;
h2=exp(-zeta*omega0*t2)*sin(omegad*t2)/(m*omegad);
doth2=exp(-zeta*omega0*t2)*(cos(omegad*t2)-zeta*omega0/omegad*sin(omegad*t2))/m;
H2=(1/m-doth2-2*zeta*omega0*h2)/omega0^2;
else
H2=0;
end
x=-f0*H2+f0*(t0/m+h1-h+2*zeta*omega0*(H1-H))/(Dt*omega0^2);
x=x+exp(-zeta*omega0*t)*(x0*cos(omegad*t)+(dotx0+zeta*omega0*x0)*sin(omegad*t)/omegad);
tt=[tt
t];
xx=[xx
x];
x=fact*x;
yf=[0
-2*b+(1+x)*yf0
-6*b+(1+x)*yf0(size(yf0,1))];
clf;
figure(1);
subplot(2,1,1)
h1=plot(xH,yH,'r');
hold on
h2=plot(xH,yH-6*b+yf0(size(yf0,1))-r,'k');
h3=plot(xf,yf,'r');
h4=plot(4*a+xd1,-3*b+yd1,'r');
h5=plot(4*a*[1 1]',-3*b*[0 1]','r');
hej=yf(size(yf,1));
h6=plot(4*a+xd2,(-7*b+yf(size(yf,1))-hej)*ones(2,1),'r');
h7=plot(4*a*[1 1]',[-7*b+yf(size(yf,1))-hej yf(size(yf,1))]','r');
h8=plot(xSQ,yf(size(yf,1))+ySQ,'r');
hold off
axis([-2 5 -10*b+(1+fact*x0)*yf0(size(yf0,1))-2*r r]);
subplot(2,1,2)
h9=plot(xH,yH,'k');
hold on;
h10=plot(tt,-xx,'r');
hold off;
axis([ 0 nstep*dt0 -xmax xmax])

% start loop
for i=1:nstep

t=i*dt0;
t0=min([t Dt]);
t1=t-t0;
h=exp(-zeta*omega0*t)*sin(omegad*t)/(m*omegad);
doth=exp(-zeta*omega0*t)*(cos(omegad*t)-zeta*omega0/omegad*sin(omegad*t))/m;
H=(1/m-doth-2*zeta*omega0*h)/omega0^2;
h1=exp(-zeta*omega0*t1)*sin(omegad*t1)/(m*omegad);
doth1=exp(-zeta*omega0*t1)*(cos(omegad*t1)-zeta*omega0/omegad*sin(omegad*t1))/m;
H1=(1/m-doth1-2*zeta*omega0*h1)/omega0^2;
if t>Dt
t2=t-Dt;
h2=exp(-zeta*omega0*t2)*sin(omegad*t2)/(m*omegad);
doth2=exp(-zeta*omega0*t2)*(cos(omegad*t2)-zeta*omega0/omegad*sin(omegad*t2))/m;
H2=(1/m-doth2-2*zeta*omega0*h2)/omega0^2;
else
H2=0;
end
x=-f0*H2+f0*(t0/m+h1-h+2*zeta*omega0*(H1-H))/(Dt*omega0^2);
x=x+exp(-zeta*omega0*t)*(x0*cos(omegad*t)+(dotx0+zeta*omega0*x0)*sin(omegad*t)/omegad);

tt=[tt
t];
xx=[xx
x];
x=fact*x;
yf=[0
-2*b+(1+x)*yf0
-6*b+(1+x)*yf0(size(yf0,1))];
set(h3,'Xdata',xf);
set(h3,'Ydata',yf);
set(h4,'Xdata',4*a+xd1);
set(h4,'Ydata',-3*b+yd1);
set(h5,'Xdata',4*a*[1 1]');
set(h5,'Ydata',-3*b*[0 1]');
set(h6,'Xdata',4*a+xd2);
set(h6,'Ydata',(-7*b+yf(size(yf,1))-hej)*ones(2,1));
set(h7,'Xdata',4*a*[1 1]');
set(h7,'Ydata',[-7*b+yf(size(yf,1))-hej yf(size(yf,1))]');