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Shifted Bernstein–Legendre polynomial collocation algorithm for numerical analysis of viscoelastic Euler–Bernoulli beam with variable order fractional model

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  • Cui, Yuhuan
  • Qu, Jingguo
  • Han, Cundi
  • Cheng, Gang
  • Zhang, Wei
  • Chen, Yiming

Abstract

In this paper, a kinetic equation of Euler–Bernoulli beam is established with variable order fractional viscoelastic model. An effective numerical algorithm is proposed. This method uses a combination of shifted Bernstein polynomial and Legendre polynomial to approximate the numerical solution. The effectiveness of the algorithm is tested and verified by mathematical examples. The dynamic behavior of viscoelastic beams made of two materials under various loading conditions is studied.

Suggested Citation

  • Cui, Yuhuan & Qu, Jingguo & Han, Cundi & Cheng, Gang & Zhang, Wei & Chen, Yiming, 2022. "Shifted Bernstein–Legendre polynomial collocation algorithm for numerical analysis of viscoelastic Euler–Bernoulli beam with variable order fractional model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 361-376.
    • Handle: RePEc:eee:matcom:v:200:y:2022:i:c:p:361-376
    DOI: 10.1016/j.matcom.2022.04.035
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    References listed on IDEAS

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    1. Wang, Lei & Chen, Yi-Ming, 2020. "Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. Wang, Lei & Chen, Yiming & Cheng, Gang & Barrière, Thierry, 2020. "Numerical analysis of fractional partial differential equations applied to polymeric visco-elastic Euler-Bernoulli beam under quasi-static loads," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Meng, Ruifan & Yin, Deshun & Yang, Haixia & Xiang, Guangjian, 2020. "Parameter study of variable order fractional model for the strain hardening behavior of glassy polymers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    4. Sun, Lin & Chen, Yiming, 2021. "Numerical analysis of variable fractional viscoelastic column based on two-dimensional Legendre wavelets algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Yu, Chunxiao & Zhang, Jie & Chen, Yiming & Feng, Yujing & Yang, Aimin, 2019. "A numerical method for solving fractional-order viscoelastic Euler–Bernoulli beams," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 275-279.
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