v2_repeat.m

美国辛辛那提大学的振动教材

% v2_repeat.m  
%
% This is a script file to solve a 3 DOF system
% given the mass, damping and stiffness matrices
% in dimensionless units and plot any desired 
% frequency response function. 
%    
%**********************************************************************
% Author: Randall J. Allemang
% Date:	18-MAR-1999
% Structural Dynamics Research Lab
% University of Cincinnati
% Cincinnati, Ohio  45221-0072
% TEL:  [phone]
% FAX:  [phone]
% E-MAIL: [e-mail]
%*********************************************************************
%
clear
close all
pi=3.14159265;
plt=input('Store plots to file (Yes=1): (0)');if isempty(plt),plt=0;end;
%
%  solve 3 dof system (with damping)
%
pi=3.14159265;
mass=[1,0,0;0,1,0;0,0,1];
stiff=[3,-1,-1;-1,3,-1;-1,-1,3];    
damp=[.1,0,0;0,.1,0;0,0,.1];    
null=[0,0,0;0,0,0;0,0,0];
%    Form 2N x 2N state space equation.  
a=[null,mass;mass,damp];
b=[-mass,null;null,stiff];
% [x,d]=eig(b,-a);
[x,d]=eig(-inv(a)*b);
% Sort Modal Frequencies  
orig_lambda=diag(d);
[Y,I]=sort(imag(orig_lambda));
lambda=orig_lambda(I);
xx=x(:,I);
lambda
pause
%     Normalize x matrix to real vectors if possible
for ii=1:6
xx(1:6,ii)=xx(1:6,ii)./xx(6,ii);
end
%     Compute 'modal a' and 'modal b' matrix
ma=xx.'*a*xx;
mb=xx.'*b*xx;
%     Extract modal vectors from state-space formulation
psi(1:3,1)=xx(4:6,1);
psi(1:3,2)=xx(4:6,2);
psi(1:3,3)=xx(4:6,3);
psi(1:3,4)=xx(4:6,4);
psi(1:3,5)=xx(4:6,5);
psi(1:3,6)=xx(4:6,6);
psi
pause
%      Calculate residue matrices
A1=psi(1:3,1)*psi(1:3,1).'./ma(1,1);
A2=psi(1:3,2)*psi(1:3,2).'./ma(2,2);
A3=psi(1:3,3)*psi(1:3,3).'./ma(3,3);
A4=psi(1:3,4)*psi(1:3,4).'./ma(4,4);
A5=psi(1:3,5)*psi(1:3,5).'./ma(5,5);
A6=psi(1:3,6)*psi(1:3,6).'./ma(6,6);
resp=1;
inp=1;
residu(1) = A1(resp,inp);
residu(2) = A2(resp,inp);
residu(3) = A3(resp,inp);
residu(4) = A4(resp,inp);
residu(5) = A5(resp,inp);
residu(6) = A6(resp,inp);
A1,A2,A3,A4,A5,A6
xxx=input('Hit any key to continue');
residu
xxx=input('Hit any key to continue');
%      Calculate desired plots
om=linspace(0,5,500);
H1=residu(1)./(j.*om-lambda(1));
H2=residu(2)./(j.*om-lambda(2));
H3=residu(3)./(j.*om-lambda(3));
H4=residu(4)./(j.*om-lambda(4));
H5=residu(5)./(j.*om-lambda(5));
H6=residu(6)./(j.*om-lambda(6));
H=H1+H2+H3+H4+H5+H6;
subplot(211),semilogy(om,abs(H))
axis;
xlabel('Frequency (Rad/Sec)'),ylabel('Magnitude'),grid
title('Frequency Response Function H(1,1)')
pause
subplot(212),plot(om,angle(H))
xlabel('Frequency (Rad/Sec)'),ylabel('Phase'),grid
pause
if plt==1,print -f1 -deps v2_repeat,end;
hold off