Pull-in effect always occurs in a micro-electromechanical system, and its pull-in analysis is essential for the normal operation. This paper aims at studying the environment effect on the pull-in instability, especially the nano/micro particles in air. A fractal model is established using a fractal derivative, and the pull-in instability can be converted into a novel state of pull-in stability when the fractal dimension tends to be very small.

The variational iteration method, which has been considered as a powerful tool to various nonlinear oscillators with initial conditions, is extended to the case of the two-point boundary conditions. Two Lagrange multipliers have to be used in this modification, and their identification is same as that of the traditional one. A generalized equation for a class of highly nonlinear oscillators followed by three examples as special cases of this generalized equation are given to elucidate the effectivity of the method. The solution obtained from this modification not only exhibits outstanding resemblance with the results got numerically but when compared to the results obtained from other established methods it shows better accuracy as well.

The nano/microelectromechanical systems (N/MEMS) have been caught much attention in the past few decades for their attractive properties such as small size, high reliability, 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 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.