Abstract
Nonlinear dynamic responses of a Micro-Electro-Mechanical Systems (MEMS) mirror with sidewall electrodes are presented that are in close agreement with previously-reported experimental data. An analysis of frequency responses reveals softening behavior, and secondary resonances originated from the dominant quadratic nonlinearity. The quadratic nonlinearity is an electromechanical coupling effect caused by the electrostatic force. This effect is reflected in our mathematical model used to simulate the dynamic response of the micro-mirror. The effects of increased forcing and decreased damping on the frequency response are investigated as the mirrors are mostly used in vacuum packages. The results can predict MEMS mirror behaviors in optical devices better than previously-reported models.
Highlights
Micro-electro-mechanical systems (MEMS) are becoming mainstream using recent micro-fabrication methods
Mathematical modeling and dynamic simulation of a bi-axial MEMS mirror with sidewall and bottom electrodes are presented here that are in close agreement with the reported experimental data
The analytical model describes softening behavior and nonlinear superharmonic resonances observed in the experiment
Summary
Micro-electro-mechanical systems (MEMS) are becoming mainstream using recent micro-fabrication methods (e.g., silicon bulk micro-machining and surface micro-machining [1]). Electrostatic actuators are the most popular because of their easy fabrication, low power consumption and high driving speed [12] They require large operating voltages to create large tilting angles. Piezoelectric actuators are faster and use lower driving voltages compared to electrothermal devices [7]. Electromagnetic actuators can achieve large mechanical tilting angles [10], but at the price of a larger size Among these actuation types, the electrostatic actuator is preferred due to the ease of fabrication in large volumes. The structure of the paper is as follows: the static modeling and simulation of the MEMS mirror under electrostatic forces from sidewall and bottom electrodes is presented. Secondary resonances evident in experimental data are explained using a mathematical analysis of the equation of motion
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