Bistability criterion for electrostatically actuated initially curved micro plates

The criterion defining the geometric parameters guaranteeing bistable behavior of electrostatically actuated curved axisymmetric circular plate is established. The usage of Berger's approximation for von-Kármán nonlinear plates, combined with single degree of freedom (DOF) reduced order (RO) modeling, allowed derivation of a simple semi-analytical bistability criterion, obtained in the form of an implicit algebraic equation in terms of critical deflection and plate geometric parameters. The criterion is verified by direct numerical solutions, combined with the arc-length method. Case studies are presented, illustrating the implementation of the suggested criterion as a useful tool for the early design stage for MEMS/NEMS devices.