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Size-dependent free vibration of piezoelectric semiconductor plate

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Abstract

In this paper, the size-dependent free vibration of a piezoelectric semiconductor plate is investigated within the framework of the nonlocal theory and piezoelectric semiconductor theory. The displacement, electric potential and perturbation of electron concentration are provided based on the first-order shear deformation theory. The two-dimensional governing equations including the equations of motion, Gauss’s law and current continuity condition are obtained by introducing the plane stress assumption and integrating the three-dimensional governing equations along the thickness direction. The vibration of a simply supported piezoelectric semiconductor plate is achieved by solving the governing equations. Some numerical examples are presented to show the effect of the initial electron concentration, nonlocal parameter, plate thickness, length to thickness ratio and length to width ratio on the vibration of the piezoelectric semiconductor plate. The results indicate that the damping characteristic of the piezoelectric semiconductor plate can be effectively designed by adding the appropriate initial electron concentration. Also, both the nonlocal parameter and the geometric property have an important effect on the natural frequency and damping characteristic of the system.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 12172236, 12202289 and U21A20430), the Science and Technology Research Project of Hebei Education Department, China (No. QN2022083), and the funded project for Innovative Graduates in Shijiazhuang Tiedao University, China (YC2023030).

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Authors and Affiliations

  1. State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Qi-lin He, Chang-song Zhu, Xue-qian Fang & Jin-xi Liu

  2. Key Laboratory of Mechanical Behavior Evolution and Control of Traffic Engineering Structures in Hebei , Shijiazhuang, 050043, China

    Chang-song Zhu

  3. Department of Engineering Mechanics, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Qi-lin He & Xue-qian Fang

  4. Department of Vehicle and Electrical Engineering, Army Engineering University, Shijiazhuang Campus, Shijiazhuang, China

    Bao-hong Han

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  1. Qi-lin He
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Correspondence to Chang-song Zhu or Xue-qian Fang.

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He, Ql., Zhu, Cs., Han, Bh. et al. Size-dependent free vibration of piezoelectric semiconductor plate. Acta Mech 234, 4821–4836 (2023). https://doi.org/10.1007/s00707-023-03632-0

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  • DOI: https://doi.org/10.1007/s00707-023-03632-0

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