Homotopy perturbation method for N/MEMS oscillators

The nano/microelectromechanical systems (N/MEMS) have caught much attention in the past few decades for their attractive properties such as small size (low mass), high reliability (high thermal conductivity and high Young's modulus), batch fabrication, and low power consumption. The dynamic oscillatory behavior of these systems is very complex due to strong nonlinearities in these systems. The basic aim of this manuscript is to investigate the nonlinear vibration property of N/MEMS oscillators arising in nanotube-based N/MEMS and resonators by the homotopy perturbation method coupled with Laplace transform (also called as He-Laplace method in literature). A generalized N/MEMS oscillator is systematically studied, and a fairly accurate analytic solution is obtained. Three special cases for electrically actuated MEMS, multi-walled carbon nanotubes-based MEMS, and MEMS subjected to van der Waals attraction are considered for comparison, and a good agreement with exact solutions is observed.