An Approach to Macromodeling of MEMS for Nonlinear Dynamic Simulation

Abstract

Abstract The method of linear normal mode summation is utilized here to construct reduced order macromodels to perform the nonlinear dynamic analysis of microelectromechanical devices and systems (MEMS). The validity of the approach is illustrated with the example of a doubly clamped beam under electrostatic actuation. Using the reduced order macromodel, it is possible to observe nonlinear effects such as the frequency shift due to a DC bias voltage, and the amplitude-dependence of resonance frequency. The undamped dynamic pull-in voltage is found to be about 9% less than the quasi-static pull-in voltage. The dynamic simulation results of the macromodel are compared with those of the complete model, and it is noted here that linear normal modes provide an adequate basis to carry out the dynamic analysis with enormous computational advantage while not losing accuracy. The simulation results are also validated with the experimentally measured data for the dynamic and static pull-in voltages, and the time to pull in at voltages beyond the pull-in voltage.