A way to obtain approximate periodic solutions to nonlinear oscillators arising in a micro-electro-mechanical system (MEMS) is presented for the case of zero initial conditions and magnetostatic excitation. The frequency-amplitude relationship is derived by adopting He’s frequency formulation. The obtained analytical results are illustrated graphically. The proposed simple approach gives the fast insight into the dynamics of the singular oscillator and can be useful for design of MEMS devices.

A nonlinear oscillator arising in a micro-electro-mechanical system (MEMS) is difficult to be solved analytically due to the zero conditions. so the main objective of this work is to analyze the mathematical model of this system, and its approximate analytical solution is solved via the coupling Variational Iteration method and Laplace transform(LVIM). This method provides an efficient way to obtain the approximate nonlinear frequency and approximate solutions of MEMS. Moreover, LVIM also approximates the pull-in threshold in terms of model parameters. Finally, the results are compared with the exact one and a good result is obtained.