Parametric Resonance Based Piezoelectric Micro-Scale Resonators: Modeling and Theoretical Analysis

Abstract

In this study, a two-component auto-parametric resonator utilizing piezoelectric actuation is proposed. The resonator consists of a plate component which serves as the exciter and a beam component which serves as the oscillator. When an electric signal is applied, the plate component experiences in-plane oscillations which serve to provide axial excitation to the beam component. The system is designed to operate in auto-parametric resonance with a plate to beam principal frequency ratio of 1:2. Due to the oscillations of the beam component, a dynamic force and a moment are applied to the plate and can cause out-of-plane oscillations of the plate component. Internal-resonance can also exist between the beam oscillations and the out-of-plane vibrations of the plate component. A model is derived in order to describe these three motions and the coupling between them. By assuming single mode behavior for each motion, the model is discretized and represented with a three degree-of-freedom model. The model is solved analytically by using the method of multiple scales. Results of the perturbation method agree well with the numerical simulation. The results for the system with strong and weak coupling between the resonator components are presented and compared.