An investigation of the mechanical behavior of initially curved microplates under electrostatic actuation

Abstract

In this article, we investigate the mechanical behavior of initially curved microplates under electrostatic actuation. Microplates are essential components of many Micro-Electro-Mechanical System devices; however, they commonly undergo an initial curvature imperfection, due to the microfabrication process. Initial curvature imperfection significantly affects the mechanical behavior of microplates. In this work, we derive a dynamic analogue of the von Kármán governing equation for such plates. These equations are then used to develop a reduced order model based on the Galerkin procedure to simulate the static and dynamic behavior of the microplate. Two profiles of initial curvature commonly encountered in microfabricated structures are considered, where one assumes a variation in shape along one dimension of the plate only (cylindrical bending shape) while the other assumes a variation in shape along both dimensions of the plate. Their effects on both the static and dynamic responses of the microplates are examined and compared. We validate the reduced order model by comparing the calculated static behavior and the fundamental natural frequency with those computed by a finite element model over a range of the initial plate rise. The static behavior of the microplate is investigated when varying the DC voltage. Then, the dynamic behavior of the microplate is examined under the application of a harmonic AC voltage superimposed to a DC voltage.