BIFURCATION OF EQUILIBRIA IN MICROMACHINED ELASTIC STRUCTURES WITH ELECTROSTATIC ACTUATION

Abstract

The determination of critical actuator voltages for the onset of "pull-in" or buckling of micromachined elastic structures or microelectromechanical systems (MEMS) with a finite number of electrostatic actuators is posed as a multiparameter bifurcation problem associated with a nonlinear partial differential equation. By making suitable approximations, the problem is reduced to one involving a multiparameter family of mappings on a bounded subset of a finite-dimensional Euclidean space RP into itself. Then the problem is reposed as one involving the intersection of level sets of certain functions whose levels correspond to the variable parameters (squares of actuator voltages). A sufficient condition for fold bifurcation when the actuator voltages exceed certain critical values is deduced using simple geometric arguments. The paper concludes with a discussion on the bifurcation of equilibrium of such systems for the limiting case where the number of actuators tends to infinity.