v2_090.m

美国辛辛那提大学的振动教材

% v2_090.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-Apr-94
% Latest Revision:	22-Jan-2001
% Structural Dynamics Research Lab
% University of Cincinnati
% Cincinnati, Ohio  45221-0072
% TEL:  [phone]
% FAX:  [phone]
% E-MAIL: [e-mail]
%*********************************************************************
%
close all
clear
pi=3.14159265;

Ndof=3;
mass=[10,0,0;0,14,0;0,0,12];
stiff=[5000,-3000,0;-3000,5500,-2500;0,-2500,2500];    
damp=10.0*[5,-3,0;-3,5.5,-2.5;0,-2.5,2.5];    
null=zeros(size(mass));
%    Form 2N x 2N state space equation.  
a=[null,mass;mass,damp];
b=[-mass,null;null,stiff];
[x,d]=eig(b,-a);
% Sort Modal Frequencies  
orig_lambda=diag(d);
[Y,I]=sort(imag(orig_lambda));
lambda=orig_lambda(I);
for ii=1:6
lambda_diag(ii,ii)=lambda(ii);
end
xx=x(:,I);
%     Normalize x matrix to real vectors if possible (4th position cannot be zero)
for ii=1:6
xx(1:6,ii)=xx(1:6,ii)./xx(4,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);

lambda
xxx=input('Hit any key to continue');

psi
xxx=input('Hit any key to continue');

%     Formulate particular (forced) solution for f2(t)=-75sin(30t)
F=[0;j*75/2;0]
s=j*30
B=[mass.*s.*s + damp.*s + stiff]
Xp=inv(B)*F
xxx=input('Hit any key to continue');

%     Formulate complementary solution
Xinit=[1;0;0]
Vinit=[20;0;0]
%     Calculate particular solution at time zero
Xp0=2*real(Xp)
Vp0=2*real(s*Xp)
InitCond=[Xinit;Vinit]-[Xp0;Vp0]

A=[psi;psi*lambda_diag]

Xc=inv(A)*InitCond
xxx=input('Hit any key to continue');

ma
xxx=input('Hit any key to continue');

%      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=input('Enter response (row) DOF: (1)');if isempty(resp),resp=1;end
inp=input('Enter input (column) DOF: (1)');if isempty(inp),inp=1;end
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);
%      Calculate desired plots
om=linspace(0,50,501);
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;

xxx=input('Hit any key to continue');
subplot(211),semilogy(om,abs(H))
xlabel('Frequency (Rad/Sec)'),ylabel('Magnitude'),grid
subplot(212),plot(om,angle(H))
xlabel('Frequency (Rad/Sec)'),ylabel('Phase'),grid
title(['FRF   Input: ',num2str(inp),'   Response: ',num2str(resp)])