Shifted Legendre polynomials algorithm used for the numerical analysis of viscoelastic plate with a fractional order model

Lin Sun, Yiming Chen, Rongqi Dang, Gang Cheng and Jiaquan Xie

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 193, issue C, 190-203

Abstract: An effective numerical algorithm is presented to analyze the fractional viscoelastic plate in the time domain for the first time in this paper. The viscoelastic behavior of the plate is described with fractional Kelvin–Voigt (FKV) constitutive model in three-dimensional space. A governing equation with three independent variables is established. Ternary unknown function in the governing equation is solved by deriving integer and fractional order differential operational matrices of the shifted Legendre polynomials. Error analysis and mathematical example are presented to verify the effectiveness and accuracy of proposed algorithm. Finally, numerical analysis of the plate under different loading conditions is carried out. Effects of the damping coefficient on vibration amplitude of the viscoelastic plate are studied. The results obtained are consistent with the current reference and actual situation. It shows that shifted Legendre polynomials algorithm is suitable for numerical analysis of fractional viscoelastic plates.

Keywords: Viscoelastic plate; Fractional Kelvin–Voigt model; Governing equation; Shifted Legendre polynomial; Operational matrix; Numerical analysis (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:193:y:2022:i:c:p:190-203

DOI: 10.1016/j.matcom.2021.10.007

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