A theoretical response of the electrostatic parallel plate to constant and low-frequencyaccelerations

Abstract

A theoretical response of an electrostatic gap-closing actuator based on parallel plates toconstant and low-frequency accelerations has been derived as a function of theapplied acceleration and voltage. The nonlinear equation of motion is obtainedin a dimensionless form from the fact that the inertial and damping forces areneglected at a frequency much less than the resonant frequency of the parallel plate,and thereafter the nonlinear equation is solved for the stable inter-plate gap atthe acceleration and voltage. From the derived solution, the pull-in accelerationis obtained as a function of the applied voltage, and the pull-in voltage is alsoexpressed as a function of the acceleration. The closed-form solution is validated bycomparison with a numerical solution. The theoretical solution is in excellentagreement with the numerical results when the actuator is exposed to a constantacceleration as well as a low-frequency acceleration. The theoretical solution andpull-in acceleration and voltage thus provide guidance to prescribe operationalconstraints for devices that use the parallel plate actuator and to predict theresponse of the electrostatic gap-closing parallel plates to constant and low-frequencyacceleration.