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Eigenvector problem with complex conjugate eigenvalues

조회 수: 3 (최근 30일)
Enterprixe
Enterprixe 2017년 4월 8일
답변: Torsten 2017년 4월 10일
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

채택된 답변

Torsten
Torsten 2017년 4월 10일
null(A) might help:
https://de.mathworks.com/help/matlab/ref/null.html
Best wishes
Torsten.

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