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<p>This paper develops a more comprehensive theoretical model for functionally graded material (FGM) piezoelectric nanobeams. The model incorporates a Winkler–Pasternak linear elastic foundation and fully accounts for the effects of dynamic flexoelectric, surface effects, and higher-order electric fields. The purpose of this study is to investigate the bending behavior and free vibration characteristics of Euler–Bernoulli beam models considering functionally graded materials. The governing equations and boundary conditions are produced using Hamilton’s variational principle. The Fourier series expansion approach is used to create the analytical solution for the bending problem. Then the analytical equation for the natural frequencies is obtained using the Navier method. The bending performance, electromechanical coupling characteristics, and normalized natural frequencies of FGM piezoelectric nanobeams are all significantly impacted by higher-order electric fields, gradient index, dynamic flexoelectric effects, surface effects, and the Winkler–Pasternak elastic foundation, according to numerical analysis. For the design and optimization of micro/nano energy harvesters and resonators, this paper offers theoretical insights and references.</p>

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Bending and vibration behavior of functionally graded piezoelectric nanobeams considering dynamic flexoelectric and surface effects

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月18日

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  • Peng Wang,
  • Bai Qiang Liu,
  • Xiao Tong Peng,
  • Feng Gao

摘要

This paper develops a more comprehensive theoretical model for functionally graded material (FGM) piezoelectric nanobeams. The model incorporates a Winkler–Pasternak linear elastic foundation and fully accounts for the effects of dynamic flexoelectric, surface effects, and higher-order electric fields. The purpose of this study is to investigate the bending behavior and free vibration characteristics of Euler–Bernoulli beam models considering functionally graded materials. The governing equations and boundary conditions are produced using Hamilton’s variational principle. The Fourier series expansion approach is used to create the analytical solution for the bending problem. Then the analytical equation for the natural frequencies is obtained using the Navier method. The bending performance, electromechanical coupling characteristics, and normalized natural frequencies of FGM piezoelectric nanobeams are all significantly impacted by higher-order electric fields, gradient index, dynamic flexoelectric effects, surface effects, and the Winkler–Pasternak elastic foundation, according to numerical analysis. For the design and optimization of micro/nano energy harvesters and resonators, this paper offers theoretical insights and references.