Nonlinear Dynamics

, Volume 77, Issue 4, pp 1349–1361 | Cite as

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

  • Chin-Chia Liu
  • Chien-Hung Liu
Original Paper


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.


Squeeze-film damping effect Reynolds equation Pull-in voltage Piezoelectric layers Hybrid method 



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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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Industrial Education and TechnologyNational Changhua University of EducationChanghuaTaiwan, ROC
  2. 2.Department of Mechanical EngineeringNational Chung Hsing UniversityTaichungTaiwan, ROC

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