Hello all,
I am trying to develop MATLAB code in order to find natural frequency of beam with point masses. I am getting results from it but those were different from reference. I am trying to compare FEM results with Rayleigh-Ritz Method. I have attached below code and image for reference.
Finding natural frequencies (Eigenvalues) is easy in Matlab. It has just a simple common to do the job., i.e., eig(.).
A simple and effective way that I can recommend is the Sattler stiffness method acc. to Konrad Sattler which is optimized for truss systems with point masses.
You can e.g. look it up here:
https://books.google.at/books?id=6VGbBgAAQBAJ&lpg=PP1&hl=de&pg=PA355#v=onepage&q&f=false
In your case, a FEM based approach would allow you to generalize the code but is more complex.
1. Make a mass (M) and stiffness (K) matrix.
2. Type this in matlab: [U,Omega2] = eig(inv(M)*K);
U is mode shapes. Omega2 is square of radial natural frequencies, you might need to sort it.
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