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

Qianqian Fan, Qiumei Liu (), Yiming Chen, Yuhuan Cui (), Jingguo Qu and Lei Wang
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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

Mathematics, 2025, vol. 13, issue 4, 1-22

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.

Keywords: orthotropic plates; viscoelastic; fractional order; shifted Legendre polynomials; numerical computation; simulation of dynamics response (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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