Homotopy perturbation method for N/MEMS oscillators

Abstract

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.

Hybrid rayleigh–van der pol–duffing oscillator: Stability analysis and controller

“…Nonlinear vibration provides an interesting potential example of the mathematical description of the nonlinear behavior of many phenomena in science, physics, and practical engineering; for example, the N/MEMS system vibrates nonlinearly. [1][2][3][4][5][6][7] The nonlinear wave equation of Kundu-Mukherjee-Naskar equation can be finally converted into a Duffing-like equation. 8 Fangzhou oscillator is a generalized Duffing equation (DE) with a singular term.…”

Fractal Pull-in Stability Theory for Microelectromechanical Systems

“…The pull-in voltage analysis of the electrostatic drive device is of great significance to the efficient operation and reliability of the device. Many literatures have conducted a lot of analysis on the dynamic pull-in of MEMS models of linear materials [1][2][3][4][5]. There are many materials used to prepare electrostatic MEMS devices, and among many materials, graphene is considered an excellent material for these devices [6].…”

Modified homotopy methods for generalized fractional perturbed Zakharov–Kuznetsov equation in dusty plasma

“…Recently, an improved modification of HPM, called the parameterized homotopy perturbation method (PHPM), was proposed in [51,52]. Another formulation, called the He-Laplace method, was proposed to obtain an exact closed approximate solution of nonlinear models [53,54]. The HPM and well-known Laplace transformation method were combined to produce a highly effective technique, called the homotopy perturbation transform method (HPTM), for solving many nonlinear problems [55,56].…”