Macromodeling of the electrostatically actuated circular plate based on mode superposition method

The macromodeling method for micro-electro-mechanical system involving multiple energy domains has become a key issue for fast simulations. In this paper, a macromodeling method based on mode superposition is focused on a circular microplate subjected to distributed electrostatic force. During the construction of reduced- order model (ROM), the energy sample data are calculated by running finite-element simulations, and a nonlinear function fitting scheme is used to generate analytical functions of kinetic energy, electrostatic co-energy and strain energy in terms of mode coordinates, thus generalized motion equations can be obtained according to the Lagrange mechanics. Once the ROM has been generated, it can be reused to simulate the behaviors of the device with a series of electric driving signals. Comparing the results of ROM with the results calculated by 3-D finite element analysis, it shows that the ROM speeds up computational process without sacrificing the accuracy, and the ROM can describe some nonlinear effects such as large displacement, pull-in instability, stress stiffening, and resonant vibration.