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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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