Nonlinear mechanics of electrically actuated microplates

Abstract

The three-dimensional nonlinear mechanics and pull-in characteristics of a microplate-based microelectromechanical system (MEMS) are investigated via a multi-degree freedom energy-based technique where the in-plane and out-of-plane motions are retained in the modelling and simulations; the deformable microplate is modelled using the Kirchhoff's plate theory in conjunction with von Kármán nonlinear strains, and it is assumed to be fully clamped at all the edges; an electrical field in the form of a combination of DC and AC voltages is applied to the deformable electrode of microplate-type. The modified couple stress theory is employed to model the small-size effects. The potential energy with size-dependent characteristics, together with the deformable microplate's kinetic energy, is formulated as functions of the displacements and mechanical and geometric parameters of the system. These energy terms, along with the Rayleigh energy dissipation and the electrical potential energy, are inserted into Lagrange's equations to derive the discretised model of the microplate-based MEMS consisting of three sets of second-order coupled reduced-order models for the in-plane and out-of-plane motions. Numerical simulations are conducted for both static and dynamic responses of the MEMS device. The numerical simulations have been performed via use of the pseudo-arc-length continuation technique in conjunction with backward-differentiation-formula (BDF) (for the nonlinear analysis); the Floquet theory is used for stability analysis. An eigenvalue extraction is employed for the linear analysis. Results are shown through DC voltage-deformation and AC frequency-motion diagrams in order to highlight the motion characteristics as well as pull-in instability of the microplate-based MEMS device.