Modal analysis

[amitp]

How does CAE software packages determine mode shapes.
I can understand that there is formula to calculate natural frequency(eigenvalues).It is square root of stiffness divided by mass.
But I want to understand how the corresponding eigenvector is found.

Thanks,
Amit Kulkarni

 

[GregLocock]

Too complicated for a post, but basically

https://en.wikipedia.org/wiki/Modal_analysis_using_FEM

Since it is possible to invert matrices by hand it is entirely possible to solve simple systems by hand, and in some cases it may be possible to eyeball the correct solutions.

There are several methods for getting the mode shape for distributed systems, Rayleigh Ritz is fun.

Cheers

Greg Locock


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[amitp]

Thanks for your response, Greg!

As I stated in my post, I can understand how the eigenvalues can be calculated. I want to know how the eigenvectors are determined.

I will appreciate if any websites or books are suggested where determining mode shapes is described in more detail.

Thanks,
Amit

 

[Guest262653]

Link 1
Link2
Link3

Modal Analysis book (Amazon link)

 

[amitp]

Thanks avscorreia for your response!

I will study these links!

Thanks and Regards,
Amit Kulkarni

 

[IceBreakerSours]

The links suggested above are excellent.

I'd add the following: Analytically, you solve the Sturm-Louiville problem. Numerical approximation methods (used by FE codes) are not straightforward and one of the 'best' methods out there is the Lanczos algorithm and you have to be an advanced student to get a real feel for it.

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