Precise Prediction on Pull-In Instability of a Deformable Micro-Plate Actuated by Distributed Electrostatic Force and Approximate Closed-Form Solutions

Abstract

This study is dedicated to perform nonlinear asymptotic analysis based on the continuous thin plate model of MEMS capacitive sensor/actuator in order to predict the pull-in voltages/positions more precisely than past works. In these past studies, only discrete models without residual stress were considered. A sensor/actuator is considered in structure of two parallel electrostatically-charged flexible square plates — one thin plate in persistent vibrations to reflect external pressure and another thick plate in relative still as the backplate. The dynamic model in the form of the partial differential equation for the parallel plates is first established based on the balance among plate flexibility, residual stress and electrostatic forces. Assuming harmonic deflection for the vibrating plate clamped on boundaries, Galerkin method is used to decompose the established system p.d.e. into discrete modal equations. Solving the discrete modal equations, plate deflection can be obtained. The pull-in position is next solved from the condition that as the pull-in occurs the electrostatic attraction force on the deflected plate exceeds the elastic restoring force by the deflected plate. It is found from analysis results for some case study that the pull-in position is 1.66 μm with air gap of 3.75 μm. This predicted pull-in position is smaller than the predict position from past works, two-thirds of the gap. In addition to theoretical analysis, experiments are also conducted to verify the correctness of the established model.