Nonlinear dynamics and parameter identification of electrostatically coupled resonators

Abstract

The nonlinear coupled vibrations widely exist in coupled resonant structures, which may exhibit rich nonlinear dynamic phenomena and play a positive role in the development of advanced micromechanical devices. This article aims to theoretically investigate the influence of coupling capacitance and design error on nonlinear dynamic behavior and parameter identification in electrostatically coupled resonators. Under the fundamental frequency excitation, the 1:1 internal resonance equations to describe electrostatically coupled resonators are obtained by using Hamilton’s principle and Galerkin method. Then, introducing the homotopy idea, an improved perturbation analysis method is applied to determine the response and stability of the system for small amplitude vibration. Through bifurcation analysis, the discontinuous phenomenon of frequency response is found, and the anti-resonance theory is introduced to study the phenomenon of multi period saddle node bifurcation. Typically, we demonstrate the exploitation of the nonlinear behavior of two electrically coupled microbeam resonators to realize the wide-band vibration. Finally, a new parameter identification method is proposed with the energy transfer efficiency, and numerical experiments under the noisy environment verify the validity of the method. The results of this paper can be potentially useful in practical applications, such as wide-band filter and nonlinear sensor.