Pull-in instability of nano-switches using nonlocal elasticity theory

This paper investigates the pull-in instability of nano-switches subjected to an electrostatic force due to an applied voltage and intermolecular force within the framework of nonlocal elasticity theory to account for the small scale effect. Both the nonlinear governing equation and boundary conditions with nonlocal effect are derived. A linear distributed load model is proposed to approximate the nonlinear intermolecular and electrostatic interactions. Closed-form solutions of critical pull-in parameters are obtained for cantilever and fixed-fixed nano-beams. The freestanding behaviour of nano-beams, which is a special case in the absence of electrostatic force, is also studied. It is found that the small scale effect contributes to the pull-in instability and freestanding behaviour of cantilever and fixed-fixed nano-beams in quite different ways. The effects of gap ratio, slenderness ratio and intermolecular force are discussed in detail as well.