Free Vibration Analysis of a Nonlinearly Tapered Cone Beam by Adomian Decomposition Method

In this paper, the free vibration of a nonlinearly tapered cone beam is analyzed based on the Euler–Bernoulli hypothesis. The characteristic/eigenvalue equation and mode shape functions of the nonlinearly tapered cone beam are derived by the Adomian decomposition method for the first time. Using a modified mathematical procedure, the natural frequencies and mode shape functions of a general nonuniform beam are analytically derived. Several numerical examples for the vibration of uniform and linearly tapered cantilever beams are presented and compared with previous results to validate the accuracy and fast convergence of the present approach. The natural frequencies and mode shapes of vibration of exponentially and trigonometrically tapered cone beams with different taper ratios are presented. The present approach enables engineers to analytically analyze tapered beams of nonuniform configurations used as various structural components in a mathematically efficient way.