Modeling and simulation of microelectromechanical systems

Modeling and Simulation of Microelectromechanical Systems in Multi-Physics Fields
Mohammad I. Younis

Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the requirements for the degree of

Doctor of Philosophy in Engineering Mechanics

Ali H. Nayfeh, Chairman Saad A. Ragab Scott L. Hendricks Ziyad Masoud Donald J. Leo

June 28, 2004 Blacksburg, Virginia

Keywords: MEMS, RF Switches, Resonators, Squeeze-Film Damping, Thermoelastic Damping, Electrostatic Actuation, Dynamic Pull-in, Microplates, Microbeams, Finite Element, Singular Perturbation, Primary and Secondary Excitations Copyright 2004, Mohammad I. Younis

Modeling and Simulation of Microelectromechanical Systems in Multi-Physics Fields
Mohammad I. Younis (ABSTRACT) The first objective of this dissertation is to present hybrid numerical-analytical approaches and reduced-order models to simulate microelectromechanical systems (MEMS) in multi-physics fields. These include electric actuation (AC and DC), squeeze-film damping, thermoelastic damping, and structural forces. The second objective is to investigate MEMS phenomena, such as squeeze-film damping and dynamic pull-in, and use the latter to design a novel RF-MEMS switch. In the first part of the dissertation, we introduce a new approach to the modeling and simulation of flexible microstructures under the coupled effects of squeeze-film damping, electrostatic actuation, and mechanical forces. The new approach utilizes the compressible Reynolds equation coupled with the equation governing the plate deflection. The model accounts for the slip condition of the flow at very low pressures. Perturbation methods are used to derive an analytical expression for the pressure distribution in terms of the structural mode shapes. This expression is substituted into the plate equation, which is solved in turn using a finite-element method for the structural mode shapes, the pressure distributions,