Effects of Nonlinearities on the Steady State Dynamic Behavior of Electric Actuated Microcantilever-based Resonators

Abstract

This paper presents the dynamic behavior of microcantilever-based microresonators and compares their steady state behavior for polarized and nonpolarized systems at different levels of nonlinearities. A microcantilever, equipped with a time-varying capacitor, makes the microresonator system. The capacitor is activated by a constant polarization voltage, and an alternative actuating voltage. The partial differential equation of motion of the vibrating electrode can be reduced to a highly nonlinear parametric second order ordinary differential equation. The steady state behavior of the microresonator has been analyzed with and without polarization voltage. The main characteristic of the non-polarized model is explained by the stability of the system in parameter plane. A set of stability chart is provided to predict the boundary between the stable and unstable domains. Furthermore, the main characteristic of the polarized model is determination by the period-amplitude relationship of the system. Applying perturbation methods, analytical equations are derived to describe the frequency response of the system, which are suitable to be utilized in parameter study and design.