Modeling of Electrostatically Actuated Microplates

Electrostatically actuated microplates have been widely used in various microsensors and actuators actuated by electrostatic force. Deep knowledge of the microplates under electrostatic force and other physical quantities is extremely important for the design and optimization of the microsensors and actuators, which can largely reduce the cost and time to develop the proposed devices compared with over and over fabrication and testing in laboratory. This chapter gives a detailed illustration on the modeling methods of electrostatically actuated microplates. Three types of modeling methods are mainly discussed, that is, finite element modeling, lumped electromechanical modeling, and distributed electromechanical modeling. For the finite element modeling method, the electromechanical elements used to model the electrostatic domain and the establishment methods of finite element electromechanical models are given for electrostatically actuated microplates. The lumped electromechanical modeling method models the electrostatically actuated microplate as one-dimensional spring-mass-capacitor system, which can qualitatively analyze the collapse voltage (or pull-in voltage) and the reason why the resonant frequency shifts under electrostatic force. For the distributed electromechanical modeling method, the electromechanical coupling models for circular and rectangular microplates under electrostatic force and hydrostatic pressure are established, and explicit theoretical expressions for collapse voltage, static deflection, and capacitance variation are proposed. In addition, the distributed modeling method also focuses on the dynamic behavior analysis, especially the resonant frequency analysis of the electrostatically actuated microplate.