Macromodeling of the Electrostatically Actuated Rectangle Plate Based On Modal Projection

Abstract

The macromodeling method for the nonlinear MEMS devices has become state of the art for fast component and system level simulation. A macromodel construction method is focused in this study for a nonlinear micro-plate actuated by a distributed electrostatic force, which is based on a modal projection method. During the construction of the reduced order model (ROM), the energy date are calculated by several finite element analysis running and a nonlinear function fitting scheme is used, thus an analytical model of kinetic energy, strain energy and electrostatic co-energy of the system have been achieved. Then the generalized motion equations of the rectangle plate represented in the term of a set of general mode coordinates can be obtained according to the Lagrange Equation. This model order reduced method can take the effect of residual stress into account and has a low computational cost. Once the ROM of the device has been generated, it can be reused to simulate the quasistate and dynamics behaviors of the device over a range of different electric driving waveforms. The calculated results show that the resulting ROM can capture the static/dynamic behaviors of the electrostatically actuated rectangle plate very well.