# Rayleigh Ritz method to find natural frequencies

1. Dec 19, 2016

### GBA13

Hello everyone,

I have found an old finite element exam question in which you have to use Rayleigh Ritz method to find natural frequencies of a system. The displacement field is given as u(x,t) = q1(t)x. I'm confused as I thought that the equation U = 0.5∫ EI u''2 dx would be used (as part of the method for finding the answer) but differentiating q1(t)x twice will give 0. Am I approaching this problem is totally the wrong way?

Thanks very much!

FYI: The way I am thinking about going about this question is to use U = 0.5∫ EI u''2 dx and T = 0.5∫ m dx u°2 (where u° is the first time derivative) and then frequency2 = U/T