Free vibration of non-uniform euler-bernoulli beams by the adomian modified decomposition method

An innovative solver for the free vibration of an elastically restrained non-uniform Euler-Bernoulli beam with tip mass of rotatory inertia and eccentricity resting on an elastic foundation and subjected to an axial load is proposed. The technique we have used is based on applying the Adomian modified decomposition method (AMDM) to our vibration problems. By using this method, any ith natural frequencies can be obtained one at a time and some numerical results are given to illustrate the influence of the physical parameters on the natural frequencies of the dynamic system. 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 simples and more straightforward than the other analyses.