A homotopy perturbation analysis of nonlinear free vibration of Timoshenko microbeams

This paper uses He's Homotopy Perturbation Method (RPM) to analyze the nonlinear free vibrational behavior of clamped-clamped and clamped-free miorobeams considering the effects of rotary inertia and shear deformation. Galerlcin's projection method is used to reduce the governing nonlinear partial differential equation. to a nonlinear ordinary differential equation. HPM is used to find analytic expressions for nonlinear natural frequencies of the pre-stretched microbeam. A parametric study investigated the effects of design parameters such as applied axial loads and slenderness ratio. The effect of rotary inertia and shear deformation on the nonlinear natural frequency was investigated. For verification, a numerical approach was implemented to solve the nonlinear equation. of vibration. A comparison between analytical and numerical results shows that HPM can predict system nonlinear vibrational behavior significantly more accurately than previously used methods in the literature.