Equivalent spring constant of rigid bodies

[mahavidyas]

Hello everyone.

I have a problem...I'm calculating natural frequency of a standing cylinder.
In order to do that, I need the k_e - equivalent spring constant of that cylinder.

k_e = (E_Y * s) / (h)

E_Y is Young's elastic modulus for material cylinder's made of
s is the cross section of cylinder
h is the height of cylinder

The cylinder is not considered "very long".
When I find k_e, I don't have any troubles finding the natural frequency.

I just want to know how is this equivalent spring constant derived?
And, is it possible to apply the same approach for other rigid bodies...ie rectangular prism.

 

[mahavidyas]

Anyone :)