Euler Bernoulli to second order ode

AI Thread Summary
The discussion focuses on the simplification of a cantilever beam's dynamics into a spring-mass system when analyzing tip movement at the first eigenmode frequency. The original poster seeks references or papers that provide proof of this concept. A suggested resource is provided, which may clarify the fundamentals and include references for further exploration of the proofs. The inquiry highlights the need for foundational literature in structural dynamics. This topic is essential for understanding beam behavior under specific excitation conditions.
umarkhan
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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.
 
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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
 

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