Pull-in behaviour of a micro switch actuated by the electrostatic under a uniform longitudinal magnetic field based on nonlocal couple stress theory

Today the micro electromechanical systems industry is widely developed. This article aims to study static pull-in instability of a clamped micro-switch which is exerted by an electric potential difference in presence of a longitudinal magnetic field. The size dependent nonlocal couple stress theory in framework of Bernoulli-Euler beam hypothesis is utilized to model a clamped micro-switch. The equilibrium equation of micro-beam in micro-switch is derived using the principle of virtual work. To obtain the dimensionless pull-in voltage of micro-switch, the equilibrium equation is solved by Galerkin method. The effect of longitudinal magnetic field and some geometric parameter of micro-beam on the pull-in voltage is studied, taking into account the effects of a set of size dependent factors with and without considering the fringing field. The results from developed model are validated by comparing them with benchmark results.