Nonlinear behavior modeling of SOI micromechanical free-free beam resonators

Abstract

Nonlinear behavior of a capacitively driven and sensed micromechanical free-free beam resonator is characterized, modeled and experimentally verified in this paper. Both the mechanical and electrostatic nonlinear effects are included in the resonator model. Instead of using the FEM tools which introduces uncertainties to the simulation process, an alternative semi-analytic method is proposed to identify the resonator parameters from just a few preliminary testing results. A 615kHz free-free beam resonator was designed, fabricated and studied. From the experimental results, it is observed that the nonlinear effects in the free-free beam always shift the resonant peak of the beam to a higher frequency under nonlinear vibration. In order to validate the proposed modeling approach, a nonlinear model was constructed based on the experimentally extracted parameters and numerically solved in MATLAB. The simulation results were compared with the experimental data, showing that the measured large-signal frequency domain response can be accurately reproduced by simulation. Although this work focused on the free-free beam resonator, the proposed modeling approach is not specific to flexural designs, but is valid for all types of electrostatic resonators. Such a method to predict nonlinear effects of microresonators will be especially useful for MEMS oscillator and filter applications.