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Double Hopf bifurcation of composite laminated piezoelectric plate subjected to external and internal excitations

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Abstract

The double Hopf bifurcation of a composite laminated piezoelectric plate with combined external and internal excitations is studied. Using a multiple scale method, the average equations are obtained in two coordinates. The bifurcation response equations of the composite laminated piezoelectric plate with the primary parameter resonance, i.e., 1:3 internal resonance, are achieved. Then, the bifurcation feature of bifurcation equations is considered using the singularity theory. A bifurcation diagram is obtained on the parameter plane. Different steady state solutions of the average equations are analyzed. By numerical simulation, periodic vibration and quasi-periodic vibration responses of the composite laminated piezoelectric plate are obtained.

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Acknowledgements

The authors gratefully acknowledge the support of the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the jurisdiction of Beijing.

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Authors and Affiliations

  1. Mathematics Science College, Inner Mongolia Normal University, Hohhot, 010022, China

    Yan Zhou

  2. Beijing Key Laboratory on Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, China

    Wei Zhang

Authors
  1. Yan Zhou
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  2. Wei Zhang
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Corresponding author

Correspondence to Yan Zhou.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11402127, 11290152 and 11072008)

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Zhou, Y., Zhang, W. Double Hopf bifurcation of composite laminated piezoelectric plate subjected to external and internal excitations. Appl. Math. Mech.-Engl. Ed. 38, 689–706 (2017). https://doi.org/10.1007/s10483-017-2196-9

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  • DOI: https://doi.org/10.1007/s10483-017-2196-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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