Pull-in dynamics of electrostatically actuated bistable micro beams

Bistable micro and nano structures integrated into microsystems exhibit clear functional advantages including the existence of several stable configurations at the same actuation force, extended working range and tunable resonant frequencies. In this work, after a short review of various operational principles of bistable micro devices, we present results of a theoretical investigation of the transient dynamics of an initially curved bistable micro beam actuated by distributed electrostatic and inertial forces. The unique combination of mechanical and electrostatic nonlinearities results in the existence of sequential mechanical (snap-through) and electrostatic (pull-in) instabilities. A phase plane analysis performed using a consistently derived lumped model along with the numerical reduced order model results indicate that the dynamic character of loading may have significant influence on the stability range of the beam. 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.