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Nonlinear forced vibration of thermo-electro-elastic piezoelectric-graphene composite nanoplate based on viscoelastic foundation

热-电-弹压电/石墨烯复合纳米板在粘弹性地基上的非线性受迫振动

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Abstract

The dynamic behavior of a piezoelectric-graphene compound asymmetric nanoplate resting on a viscoelastic foundation is investigated in this paper, considering both exposure to thermal environment and transverse harmonic excitation. First, according to the Hamilton principle and nonlocal elastic theory, a dynamic model of the composite nanoplate is established by a group of nonlinear partial differential equations. Through the Galerkin method, the simply supported partial differential equations form of the composite nanoplate system is simplified to the form of an asymmetric Duffing-Helmholtz oscillator. Then, the dynamic mechanism of the composite nanoplate system containing a quadratic nonlinear term is revealed, and the influences of nonlocal parameter, temperature, viscoelastic foundation, thickness, aspect ratio and external voltage on the nonlinear vibration of the system are numerically analyzed comprehensively. Moreover, the effect of wave number on nonlinear vibration compared with the first-order wavenumber is emphasized. It is anticipated that the dynamic results of the present work would provide the theoretical basis for the experimental characterization of the mechanical properties of piezoelectric-graphene composite nanoresonators.

摘要

本文研究了非对称压电/石墨烯复合纳米板在粘弹性地基上、热环境及外部简谐激励作用下的动力学行为. 根据Hamilton原理和Kirchhoff板理论, 建立复合纳米板的动力学方程, 并通过Galerkin方法对简支边界下的动力学方程进行求解, 获得了一个包含有二次非线性项的Duffing-Helmholtz方程. 从解析和数值方面分别分析了非局部弹性参数、温度、粘弹性基体、电压以及纳米板的几何尺寸对系统非线性与线性频率比和非线性振动行为的影响. 此外, 本文揭示了系统的非对称性和二次非线性项之间的对应关系. 本研究的动力学结果将为压电-石墨烯复合纳米谐振器力学性能的实验表征提供理论依据.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11872303, 12072262, 11972287, and 12172283).

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Authors and Affiliations

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an, 710072, China

    Yunping Zhao  (赵云平), Shuo Zhang  (张硕), Tongtong Sun  (孙彤彤) & Lin Du  (都琳)

  2. Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an, 710072, China

    Xiuhui Hou  (侯秀慧) & Zichen Deng  (邓子辰)

  3. Ministry of Industry and Information Technology Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi’an, 710072, China

    Zichen Deng  (邓子辰)

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  1. Yunping Zhao  (赵云平)
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  2. Xiuhui Hou  (侯秀慧)
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  5. Lin Du  (都琳)
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  6. Zichen Deng  (邓子辰)
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Correspondence to Zichen Deng  (邓子辰).

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Author contributions

Yunping Zhao and Xiuhui Hou designed the research. Yunping Zhao wrote the first draft of the manuscript and numerical modeling. Tongtong Sun helped examine the manuscript. Xiuhui Hou and Yunping Zhao discussed and revised the final version. Xiuhui Hou, Shuo Zhang, Lin Du and Zichen Deng supported the paper by the foundation. Zichen Deng gave the financial support.

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Zhao, Y., Hou, X., Zhang, S. et al. Nonlinear forced vibration of thermo-electro-elastic piezoelectric-graphene composite nanoplate based on viscoelastic foundation. Acta Mech. Sin. 39, 522228 (2023). https://doi.org/10.1007/s10409-022-22228-x

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