Nonlinear behaviour of electrically actuated microplate-based MEMS resonators

This paper is the first which examines the nonlinear dynamical characteristics of an imperfect microplate-based microelectromechanical system (MEMS), taking into account geometric nonlinearities, geometric imperfections, small-size effects, and all the transverse and in-plane inertia and displacements. The deformable electrode (microplate) is fully clamped and subject to a combination of DC and AC voltages. A Kirchhoff plate theory, along with von Kármán nonlinear strains, is employed to model the initially slightly curved microplate. The coupling between restoring force and electrical field is formulated via displacement/electrical nonlinearities in the oscillation model of the electrically actuated microsystem. The Lagrange equations are used in order to dynamically balance the structural, electrical, and kinetic energies of the microsystem. Numerical simulations are performed by means of a weighted-residual method together with a continuation method coupled with backward differentiation formula (BDF). In order to analyse the nonlinear electrostatic/dynamic characteristics of the deformable microplate (electrode), the AC voltage is set to zero, and the DC voltage is increased and the electrostatic deflection of the deformable microplate is obtained and the pull-in characteristics are analysed; the influences of the initial imperfection and small-size parameter are also investigated on the electrostatic pull-in of the microsystem. For the deformable microplate subjected to both DC and AC voltages, the AC frequency-oscillation characteristics of the microsystem are examined; it is examined that how initial imperfection in the deformable microplate affects the nonlinear vibrational behaviour and the jump phenomena.