Pull-in instability of geometrically nonlinear micro-switches under electrostatic and Casimir forces

This paper investigates the pull-in instability of micro-switches under the combined electrostatic and intermolecular forces and axial residual stress, accounting for the force nonlinearity and geometric nonlinearity which stems from mid-plane stretching. The micro-switch considered in the present study is made of either homogeneous material or non-homogeneous functionally graded material with two material phases. Theoretical formulations are based on Euler-Bernoulli beam theory and von Karman type nonlinear kinematics. The principle of virtual work is used to derive the nonlinear governing differential equation which is then solved using the differential quadrature method (DQM). Pull-in voltage and pull-in deflection are obtained for micro-switches with four different boundary conditions (i.e. clamped-clamped, clamped-simply supported, simply supported and clamped-free). The present solutions are validated through direct comparisons with experimental and other existing results reported in previous studies. A parametric study is conducted, focusing on the combined effects of geometric nonlinearity, gap ratio, slenderness ratio, Casimir force, axial residual stress and material composition on the pull-in instability