Free vibration analysis of multiple-stepped beams by using Adomian decomposition method

The Adomian decomposition method (ADM) is employed in this paper to investigate the free vibrations of the Euler–Bernoulli beams with multiple cross-section steps. The proposed ADM method can be used to analyze the vibration of beams consisting of an arbitrary number of steps through a recursive way. The solution can be obtained by solving a set of algebraic equations with only three unknown parameters. Furthermore, the method can be extended to obtain an approximate solution to vibration problems of any type of non-uniform beams. Several numerical examples are presented and compared to those given in the paper. It is shown that the ADM offers an accurate and effective method of free vibration analysis of multiple-stepped beams with arbitrary boundary conditions.