Free vibration of non-uniform Euler–Bernoulli beams with general elastically end constraints using Adomian modified decomposition method

This paper deals with free vibration problems of non-uniform Euler–Bernoulli beam under various supporting conditions. The technique we have used is based on applying the Adomian modified decomposition method (AMDM) to our vibration problems. Doing some simple mathematical operations on the method, we can obtain ith natural frequencies and mode shapes one at a time. The computed results agree well with those analytical and numerical results given in the literatures. These results indicate that the present analysis is accurate, and provides a unified and systematic procedure which is simple and more straightforward than the other modal analysis.