Initially curved microplates under electrostatic actuation: theory and experiment

Abstract

Microplates are the building blocks of many micro-electro-mechanical systems. It is common for them to experience initial curvature imperfection due to residual stresses caused by the micro fabrication process. Such plates are essentially different from perfectly flat ones and cannot be modeled using flat plate models. In this paper, we adopt a dynamic analog of the von Karman governing equations of imperfect 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 under electrostatic actuation. To validate the simulation results, an initially curved imperfect microplate made of silicon nitride is fabricated and tested. The static behaviour of the microplate is investigated when applying a DC voltage V dc . Then, the dynamic behaviour of the microplate is examined under the application of a harmonic AC voltage, V ac , superimposed to V dc . The simulation results show good agreement with the experimentally measured responses.

On the response of MEMS resonators under generic electrostatic loadings: experiments and applications

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Voltage-Induced Snap-Through of an Asymmetrically Laminated, Piezoelectric, Thin-Film Diaphragm Micro-Actuator—Part 1: Experimental Studies and Mathematical Modeling

“…3(a)). Therefore, the electric potential /ðx; y; z ð2Þ ; tÞ in layer S ð2Þ is a union of the electric potentials established by the inner and outer electrodes, i.e., /ðx; y; z ð2Þ ; tÞ ¼ / À ðx; y; z ð2Þ ; tÞ [ / þ ðx; y; z ð2Þ ; tÞ (13) where the superscripts À and þ refer to the inner and outer electrodes, respectively. Based on Assumption 7, the electric potential varies linearly across the thickness direction.…”

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