An innovative eigenvalue problem solver for free vibration of uniform Timoshenko beams by using the Adomian modified decomposition method

This paper deals with free vibration problems of uniform Timoshenko beams under various supporting boundary 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 literature. These results indicate that the present analysis is accurate, and provides a unified and systematic procedure which is simpler and more straightforward than the other modal analysis.