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Analysis of nonlinear dynamic behavior of electrically actuated micro-beam with piezoelectric layers and squeeze-film damping effect

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Abstract

An analytical model based on a nonlinear deflection equation and the Reynolds equation is proposed to describe the dynamic behavior of an electrically actuated micro-beam with two piezoelectric layers. The proposed model takes explicit account of the fringing field effect, the axial stress effect, the residual stress effect, and the squeeze-film damping effect between the micro-beam and the lower electrode. The nonlinear governing equation of the micro-beam is solved using a hybrid computational scheme comprising the differential transformation method and the finite difference method. The validity of the analytical model and numerical solution procedure is demonstrated by comparing the result obtained for the pull-in voltage of a micro-beam actuated by a DC voltage only with that presented in the literature. It is shown that the nonlinear dynamic response of the micro-beam can be controlled using a combined driving scheme consisting of both the magnitude and the frequency of the AC actuating voltage and a DC driving voltage. The effects of the AC/DC actuating conditions, micro-beam geometry parameters, and squeeze-film damping force on the center-point displacement of the micro-beam are systematically examined. In addition, the actuating conditions which ensure the stability of the micro-beam are identified by means of phase portraits and Poincaré maps. In general, the results show that the analytical model and hybrid numerical scheme provide a feasible means of analyzing the dynamic response of a variety of electrostatically-actuated microstructures.

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Acknowledgments

The authors gratefully acknowledge the financial support provided to this study by the National Science Council of Taiwan under Grant Number NSC 101-2221-E-018 -007.

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Authors and Affiliations

  1. Department of Industrial Education and Technology, National Changhua University of Education, Bao-Shan Campus: Number 2, Shi-Da Road, Changhua, 500, Taiwan, ROC

    Chin-Chia Liu

  2. Department of Mechanical Engineering, National Chung Hsing University, Taichung, Taiwan, ROC

    Chien-Hung Liu

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  1. Chin-Chia Liu
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Correspondence to Chin-Chia Liu.

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Liu, CC., Liu, CH. Analysis of nonlinear dynamic behavior of electrically actuated micro-beam with piezoelectric layers and squeeze-film damping effect. Nonlinear Dyn 77, 1349–1361 (2014). https://doi.org/10.1007/s11071-014-1384-3

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  • DOI: https://doi.org/10.1007/s11071-014-1384-3

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