Eigenvector problem with complex conjugate eigenvalues

Question

Enterprixe 2017-4-8

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/334378-eigenvector-problem-with-complex-conjugate-eigenvalues

回答： Torsten 2017-4-10

Hello, im solving here a viscous damping problem. As you can see det(A) is the equation that must be solved in order to obtain the eigenvalues of the problem. My issue is after having all 10 eigenvalues (20 with their conjugates) i do not know exactly how to make MATLAB calculate me the eigenvectors of the problem, given that im not using the 'eig' command.

M=[1 0 0 0 0 0 0 0 0 0;           
   0 1 0 0 0 0 0 0 0 0;
   0 0 1 0 0 0 0 0 0 0;
   0 0 0 1 0 0 0 0 0 0;
   0 0 0 0 1 0 0 0 0 0;
   0 0 0 0 0 2 0 0 0 0;
   0 0 0 0 0 0 3 0 0 0;
   0 0 0 0 0 0 0 3 0 0;
   0 0 0 0 0 0 0 0 4 0;
   0 0 0 0 0 0 0 0 0 1];
K=[1 -1 0 0 0 0 0 0 0 0;           
  -1 3 0 0 0 0 -2 0 0 0;
   0 0 3 -1 0 0 0 -2 0 0;
   0 0 -1 1 0 0 0 0 0 0;
   0 0 0 0 1 -1 0 0 0 0;
   0 0 0 0 -1 3 -2 0 0 0;
   0 -2 0 0 0 -2 8 -4 0 0;
   0 0 -2 0 0 0 -4 11 -5 0;
   0 0 0 0 0 0 0 -5 10 -5;
   0 0 0 0 0 0 0 0 -5 5];
F=[1 -1 0 0 0 0 0 0 0 0;
   -1 2 0 0 0 0 -1 0 0 0;
   0 0 0 0 0 0 0 0 0 0;
   0 0 0 0 0 0 0 0 0 0;
   0 0 0 0 0 0 0 0 0 0;
   0 0 0 0 0 0 0 0 0 0;
   0 -1 0 0 0 0 2 -1 0 0;
   0 0 0 0 0 0 -1 1 0 0;
   0 0 0 0 0 0 0 0 0 0;
   0 0 0 0 0 0 0 0 0 0];
f=2/50;
m=8;
k=2000; 
Mv=m*M;
Fv=f*F;
Kv=K*k;
syms s phi
A=s^2*Mv +s*Fv+ Kv;
r=det(A);
s=double(subs(solve(r)));
for i=1:20
   A=s(i)^2*Mv +s(i)*Fv+ Kv;
   eqn= A*phi==0;
   Mod(i)=double(subs(solve(eqn,phi)));
   end