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Fractional modelling and numerical simulations of variable-section viscoelastic arches

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  • Dang, Rongqi
  • Chen, Yiming

Abstract

In this paper, two fractional viscoelastic constitutive models are used to establish nonlinear fractional integro-differential governing equations of variable-section viscoelastic arches. Shifted Chebyshev polynomial algorithm is introduced to numerically solve the governing equations directly in time domain. The feasibility and accuracy of the proposed algorithm are verified by convergence analysis and error estimation of a mathematical example. In addition, the dynamic responses of variable-section viscoelastic arches with three materials under two fractional models are also studied to verify the effectiveness of shifted Chebyshev polynomial algorithm.

Suggested Citation

  • Dang, Rongqi & Chen, Yiming, 2021. "Fractional modelling and numerical simulations of variable-section viscoelastic arches," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    • Handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321004653
    DOI: 10.1016/j.amc.2021.126376
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    References listed on IDEAS

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    6. 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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    Cited by:

    1. Zheng, Bibo & Wang, Zhanshan, 2022. "Mittag-Leffler synchronization of fractional-order coupled neural networks with mixed delays," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    2. Li Jiang & Tao Wang & Qing-Xue Huang, 2023. "Resonance Analysis of Horizontal Nonlinear Vibrations of Roll Systems for Cold Rolling Mills under Double-Frequency Excitations," Mathematics, MDPI, vol. 11(7), pages 1-15, March.

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