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Research Papers

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

[+] Author and Article Information
Andrew J. Dick

e-mail: Andrew.J.Dick@rice.edu
Nonlinear Phenomena Laboratory,
Department of Mechanical Engineering,
Rice University, Houston, TX 77005

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 30, 2011; final manuscript received March 7, 2012; published online June 14, 2012. Assoc. Editor: Carmen M. Lilley.

J. Comput. Nonlinear Dynam 8(1), 011004 (Jun 14, 2012) (9 pages) Paper No: CND-11-1106; doi: 10.1115/1.4006429 History: Received June 30, 2011; Revised March 07, 2012

In this study, a two-component autoparametric 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 autoparametric 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. The possibility of internal-resonance between the beam oscillations and the out-of-plane vibrations of the plate component are also considered. 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 and results are verified with the numerical simulations. Also, the influence of system parameters on response behavior is studied and the ideal operational conditions and parameter values for nominal performance are obtained.

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Figures

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Fig. 1

Conceptual diagram of the proposed micro-scale resonators. The electrode layers will be patterned to electrically isolate the plate and beam components for specific applications.

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Fig. 2

Frequency-response of the beam obtained by using the method of multiple scales (MMS) and numerical simulations performed by using matlab for the nominal parameter values

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Fig. 3

Frequency-response curves for different levels of nonlinear damping in the beam

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Fig. 4

Frequency-response curves for different levels of in-plane frequency mis-tuning. Applied voltage magnitude is increased to Q=0.07.

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Fig. 5

Stability wedge curves for different in-plane mis-tuning parameter values. The curves for negative values are the mirror image of their corresponding positive plots.

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Fig. 6

Frequency-responses of the beam component (a) and the plate component (b) for different in-plane mis-tuning parameter values for the system with higher coupling. Applied voltage magnitude increased to Q=0.07.

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Fig. 7

The stability wedge of the beam component for system with higher coupling

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Fig. 8

The frequency-responses of the beam component for a small plate out-of-plane damping ratio, μ1=0.002 (top) and μ1=0.001 (Bottom). Red dashed portions are unstable.

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