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I have a wall with the bottom end of it fixed to the ground. I want to derive from first principles the frequencies and mode shapes of the structure.

I know that I will need to start with the following formula:

$K-\omega^2M=0$

And I know how to do that for a cantilever column.

But wall is a different thing than column because it is an area element instead of a line element. And I don't know how to generate the correct expression for $K$ and $M$ for a continuum area element.

How to proceed with the analytical solution for wall eigenvalue analysis?

Note: I am not looking for a FEM solution.

Graviton
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1 Answers1

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Your "wall" would be referred as a "plate" in the technical literature. The eigenvalue problem for a plate is significantly more complicated than a beam, but similar ideas.

I would suggest that you look for a book on "vibrations of continuous systems", for example: http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471771716.html

There are also specific books dedicated entirely to plates, e.g. https://www.crcpress.com/Vibrations-of-Shells-and-Plates-Third-Edition/Soedel/p/book/9780824756291 however they may be hard to understand without sufficient background.

Daniel K
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