Pull-In Dynamics of Electrostatically Actuated Bistable Micro Beam

Abstract

Results of theoretical investigation of the transient dynamics of an initially curved electrostatically actuated clamped-clamped micro beam are presented. A reduced order model of the shallow Euler-Bernoulli arch developed using the Galerkin procedure with eigenmodes of a straight beam as a basis accounts for the distributed electrostatic and inertial loading, fringing electric fields and nonlinear squeeze film damping. Due to the unique combination of mechanical and electrostatic nonlinearities which is intrinsic in micro devices but is not encountered naturally in large-scale structures, the voltage-deflection characteristic of the sufficiently curved beam may have two maxima implying the existence of sequential mechanical (snap-through) and electrostatic (pull-in) instabilities. Phase plane analysis performed for the case of a suddenly applied electrostatic loading along with the simulation results show that critical voltages corresponding to the dynamic snap-through and pull-in instabilities are lower than their static counterparts while the minimal curvature required for the appearance of the dynamic snap-through is higher than in the static case. Clear functional advantages of this kind of structures, namely extended stable deflections and ability to tune the device frequencies in a very large range may result in improved performance of switches, inertial sensors and micromechanical non-volatile memory devices.