UC Berkeley

Microelectromechanical systems (MEMS) often make use of a type of plate-based electrostatic actuator that can, under certain conditions, come into contact with a dielectric-coated electrode. After this “touchdown,” the presence of a free boundary between the contacting and non-contacting regions of the plate induces strong nonlinearities in the system, significantly affecting its dynamics. In this paper we construct and analyze the mechanics of an idealized actuator after touchdown, focusing especially on the case where the dielectric is very thin and neglecting as many sources of nonlinearity as feasible in order to isolate the effect of contact. After characterizing the static equilibria, we construct a reduced-order dynamic model and investigate its application to the problem of vibration-assisted stiction repair, in which structural vibrations are employed to release the actuator from the touchdown configuration. This model has several features that are interesting in their own right, including a saddle–node bifurcation and finite-time blow-up. Our approach synthesizes concepts from configurational mechanics, fracture mechanics, and nonlinear dynamics, and serves as a blueprint for constructing more sophisticated models of touchdown dynamics that incorporate important practical effects.