Nonlinear free vibration of simply supported beams considering the effects of shear deformation and rotary inertia, a homotopy perturbation approach

Abstract

The objective of this paper is to apply He's homotopy perturbation method (HPM) to analyze nonlinear free vibration of simply supported Timoshenko beams considering the effects of rotary inertia and shear deformation. First, the equation governing the nonlinear free vibration of a Timoshinko beam is nondimensionalized. Galerkin's projection method is utilized to reduce the governing nonlinear partial differential equation to a nonlinear ordinary differential equation. HPM is then used to find analytic expressions for nonlinear natural frequencies of the pre-stretched beam. A parametric study has also been applied in order to investigate the effects of design parameters such as applied axial load and slenderness ratio. Comparison between presented results and numerical results which are in full agreement shows that HPM can significantly improve the accuracy of previously reported results in the literature.