Dynamics of a nonlinear microresonator based on resonantly interacting flexural-torsional modes

Ashwin Vyas, Purdue University
Dimitrios Peroulis, Birck Nanotechnology Center and School of Electrical and Computer Engineering, Purdue University
Anil Bajaj, Purdue University

Date of this Version

October 2008


Nonlinear Dyn (2008) 54: 31–52

This document has been peer-reviewed.



A novel microresonator operating on the principle of nonlinear modal interactions due to autoparametric 1:2 internal resonance is introduced. Specifically, an electrostatically actuated pedal-microresonator design, utilizing internal resonance between an out-of-plane torsional mode and a flexural in-plane vibrating mode is considered. The two modes have their natural frequencies in 1:2 ratio, and the design ensures that the higher frequency flexural mode excites the lower frequency torsional mode in an autoparametric way. A Lagrangian formulation is used to develop the dynamic model of the system. The dynamics of the system is modeled by a two degrees of freedom reduced-order model that retains the essential quadratic inertial nonlinearities coupling the two modes. Retention of higher-order model for electrostatic forces allows for the study of static equilibrium positions and static pull-in phenomenon as a function of the bias voltages. Then for the case when the higher frequency flexural mode is resonantly actuated by a harmonically varying AC voltage, a comprehensive study of the response of the microresonator is presented and the effects of damping, and mass and structural perturbations from nominal design specifications are considered. Results show that for excitation levels above a threshold, the torsional mode is activated and it oscillates at half the frequency of excitation. This unique feature of the microresonator makes it an excellent candidate for a filter as well as a mixer in RF MEMS devices.