Approaches for Reduced Order Modeling of Electrically Actuated von Karman Microplates

Abstract

This article presents and compares different approaches to develop reduced order models for the nonlinear von Karman rectangular microplates actuated by nonlinear electrostatic forces. The reduced-order models aim to investigate the static and dynamic behavior of the plate under small and large actuation forces. A fully clamped microplate is considered. Different types of basis functions are used in conjunction with the Galerkin method to discretize the governing equations. First we investigate the convergence with the number of modes retained in the model. Then for validation purpose, a comparison of the static results is made with the results calculated by a nonlinear finite element model. The linear eigenvalue problem for the plate under the electrostatic force is solved for a wide range of voltages up to pull-in. Results among the various reduced-order modes are compared and are also validated by comparing to results of the finite-element model. Further, the reduced order models are employed to capture the forced dynamic response of the microplate under small and large vibration amplitudes. Comparison of the different approaches are made for this case. Keywords: electrically actuated microplates, static analysis, dynamics of microplates, diaphragm vibration, large amplitude vibrations, nonlinear dynamics