Electrostatic nonlinear dispersive parametric mode interaction

Abstract

Understanding and controlling the nonlinear coupling in micro/nanomechanical resonators are of great importance to the exploitation of advanced devices. The recently observed electrostatic nonlinear parametric coupling is a very interesting topic. However, the theoretical model of the electrostatic parametric coupling remains unclear. This paper explicitly derives the model and the electrostatically induced dispersive parametric coupling which reveals the ability to tune the bifurcation topology of capacitive resonators is analyzed based on the multiple-time-scale method. A novel displacement-to-frequency transduction scheme based on this electrostatic dispersive parametric coupling effect is proposed. The transduction sensitivity is theoretically given, which indicates that this electrostatic dispersive transduction scheme can provide even more design freedoms than the existing displacement-to-frequency transduction scheme based on tension modulation. In addition, a bifurcation reversal effect is predicted in the strong actuated states of the dispersive parametric coupled system, which reveals the ability to tune the bifurcation topology of capacitive resonators.