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Subject: Re: Help!!! Eigenvalue program for frequency dependent matrix
Date: Wed, 9 Jul 2008 05:32:02 +0000 (UTC)
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"Yogesh " <yahoo@trashmail.net> wrote in message
<g51ddf$pm4$1@fred.mathworks.com>...
> I am trying find the natural frequency of a vibration problem
> 
> The standard eigenvalue problem looks like
> 
> Kx=lMx
> 
> for which there is a simple eig(K,M) command that does the
> trick. 
> 
> The trouble is that the K matrix is frequency dependent in
> this case. So, each element of the K matrix is a function of
> frequency. How can I approach this type of a problem in
matlab?
> 
> Help will be much appreciated!! 
> 
> Thanks,
> YM

Hi

Your problem may be rewritten into the form

    K(omega).X = M.X.S

where 
K(omega) is a stiffness matrix of a system dependent on an
operational frequency (speed),
M is a mass matrix of the system,
X is a modal matrix of the system composed of modal vectors,
S is a diagonal spectral matrix with eigenvalues on diagonal.

To each operational frequency omega belong matrices X and S,
which are different from those belonging to other omega. The
system is "evolutionary". 

You wanted to solve the eigenvalue problem for omega as a
function of S. It is possible to solve it in iterations for
a single eigenvalue s_k, if you reguire that, say, omega=
real(s_k). Then, you may use the MATLAB  function fzero
applied to the difference  omega-real(s_k).

I hope that it helps.

Mira