v2_058.m

美国辛辛那提大学的振动教材

% v2_058.m   
%
% This is a script file to solve a 2 DOF system
% given the mass, damping and stiffness matrices
% in dimensionless units.  The output includes poles, 
% residues(modal coefficients) and time and frequency 
% domain plots of impulse and frequency response functions.
%  
% 2 DOF Proportionally Damped System
   
%**********************************************************************
% Author: Randall J. Allemang
% Date:	18-Apr-94
% Structural Dynamics Research Lab
% University of Cincinnati
% Cincinnati, Ohio  45221-0072
% TEL:  [phone]
% FAX:  [phone]
% E-MAIL: [e-mail]
%*********************************************************************
%
clear,clg
plt=input('Store plots to file (Yes=1): (0)');if isempty(plt),plt=0;end;
pi=3.14159265;
alpha=1.0
beta=0.005
mass=[5,0;0,10];
stiff=[4,-2;-2,6].*2000;    
damp=alpha*mass + beta*stiff;
null=[0,0;0,0];
%    Form 2N x 2N state space equation.  
a=[null,mass;mass,damp];
b=[-mass,null;null,stiff];
[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);
%     Normalize x matrix 
for ii=1:4
xx(1:4,ii)=xx(1:4,ii)./xx(3,ii);
end
%     Extract modal vectors from state-space formulation
psi(1:2,1)=xx(3:4,1);
psi(1:2,2)=xx(3:4,2);
psi(1:2,3)=xx(3:4,3);
psi(1:2,4)=xx(3:4,4);
lambda,psi     
pause
%      Calculate modal mass matrix
mm=psi.'*mass*psi;
%      Calculate modal scaling value (Q)
Q(1)=1./(2*j*imag(lambda(1))*mm(1,1));
Q(2)=1./(2*j*imag(lambda(2))*mm(2,2));
%      Calculate residue matrices
A1=Q(1).*psi(1:2,1)*psi(1:2,1).';
A2=Q(2).*psi(1:2,2)*psi(1:2,2).';
%      Formulate H(1,2) FRF as Default
resp=input('Enter response (row) DOF: (1)');if isempty(resp),resp=1;end
inp=input('Enter input (column) DOF: (2)');if isempty(inp),inp=2;end
residu(1) = A1(resp,inp);
residu(2) = A2(resp,inp);
A1,A2
pause
magA1=abs(A1);
phaseA1=angle(A1).*360.0./(2.0*pi);
magA2=abs(A2);
phaseA2=angle(A2).*360.0./(2.0*pi);
magA1,phaseA1
magA2,phaseA2
pause
lambda,residu
pause