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Studying the Dynamics Response of Viscoelastic Orthotropic Plates Based on Fractional-Order Derivatives and Shifted Legendre Polynomials

Author

Listed:
  • Qianqian Fan

    (College of Science, North China University of Science and Technology, Tangshan 063000, China)

  • Qiumei Liu

    (College of Science, North China University of Science and Technology, Tangshan 063000, China)

  • Yiming Chen

    (School of Science, Yanshan University, Qinhuangdao 066004, China)

  • Yuhuan Cui

    (College of Science, North China University of Science and Technology, Tangshan 063000, China)

  • Jingguo Qu

    (College of Science, North China University of Science and Technology, Tangshan 063000, China)

  • Lei Wang

    (College of Science, North China University of Science and Technology, Tangshan 063000, China
    LISPEN, Arts et Métiers Institute of Technology, HESAM University, F-59000 Lille, France)

Abstract

This paper primarily investigates the dynamics response of viscoelastic orthotropic plates under a fractional-order derivative model, which is efficiently simulated numerically using the FKV (Fractional Kelvin–Voigt) model and the shifted Legendre polynomial algorithm. By establishing the fractional-order governing equation and directly solving it in the time domain using a shifted Legendre polynomial, the approach achieves low error and high accuracy. The analysis shows that the load, plate thickness, and creep time all affect the plate displacement, and the fractional-order model outperforms the integer-order model to better capture the dynamics response of the material.

Suggested Citation

  • Qianqian Fan & Qiumei Liu & Yiming Chen & Yuhuan Cui & Jingguo Qu & Lei Wang, 2025. "Studying the Dynamics Response of Viscoelastic Orthotropic Plates Based on Fractional-Order Derivatives and Shifted Legendre Polynomials," Mathematics, MDPI, vol. 13(4), pages 1-22, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:4:p:622-:d:1591043
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    References listed on IDEAS

    as
    1. Sun, Lin & Chen, Yiming & Dang, Rongqi & Cheng, Gang & Xie, Jiaquan, 2022. "Shifted Legendre polynomials algorithm used for the numerical analysis of viscoelastic plate with a fractional order model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 190-203.
    2. Andrey Zvyagin & Ekaterina Kostenko, 2023. "Investigation of the Weak Solvability of One Viscoelastic Fractional Voigt Model," Mathematics, MDPI, vol. 11(21), pages 1-23, October.
    3. Fahad, Hafiz Muhammad & Fernandez, Arran, 2021. "Operational calculus for Caputo fractional calculus with respect to functions and the associated fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    Full references (including those not matched with items on IDEAS)

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