Free vibration analysis of a type of tapered beams by using Adomian decomposition method

The Adomian decomposition method (ADM) is employed in this paper to investigate the free vibrations of tapered Euler–Bernoulli beams with a continuously exponential variation of width and a constant thickness along the length under various boundary conditions. Based on ADM the governing differential equation for the tapered beam becomes a recursive algebraic equation. By using the boundary condition equations, the dimensionless natural frequencies and corresponding mode shapes can be easily obtained simultaneously. The computed results for different boundary conditions and non-uniformity ratios are presented. The accuracy is assured from the convergence and comparison published results.