Euler Bernoulli to second order ode

[umarkhan]

hello,
I have read in a number of papers that if we have a cantilever beam and are only interested in the movement of the tip when the base is being excited at the frequency of the first eigen mode , then the whole beam can be replaced by a spring mass system. Can anyone tell me of a paper or book where this is actually proved?

Thanks.

 

[timthereaper]

The paper will help clarify the basics and the references at the bottom will help in finding information on the various proofs.

http://faculty.uml.edu/pavitabile/22.403/web_downloads/Final_Project_Cantilever_101806.pdf