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

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

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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:193:y:2022:i:c:p:190-203
    DOI: 10.1016/j.matcom.2021.10.007
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    References listed on IDEAS

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    1. Cao, Jiawei & Chen, Yiming & Wang, Yuanhui & Cheng, Gang & Barrière, Thierry, 2020. "Shifted Legendre polynomials algorithm used for the dynamic analysis of PMMA viscoelastic beam with an improved fractional model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Chen, Yiming & Ke, Xiaohong & Wei, Yanqiao, 2015. "Numerical algorithm to solve system of nonlinear fractional differential equations based on wavelets method and the error analysis," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 475-488.
    3. Abbasbandy, Saeid & Kazem, Saeed & Alhuthali, Mohammed S. & Alsulami, Hamed H., 2015. "Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 31-40.
    4. Yang, Yin & Wang, Jindi & Zhang, Shangyou & Tohidi, Emran, 2020. "Convergence analysis of space-time Jacobi spectral collocation method for solving time-fractional Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 387(C).
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    Cited by:

    1. Xie, Jiaquan & Zhao, Fuqiang & He, Dongping & Shi, Wei, 2022. "Bifurcation and resonance of fractional cubic nonlinear system," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Heydari, M.H. & Razzaghi, M., 2023. "Piecewise fractional Chebyshev cardinal functions: Application for time fractional Ginzburg–Landau equation with a non-smooth solution," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).

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