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A numerical method for solving fractional-order viscoelastic Euler–Bernoulli beams

Author

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  • Yu, Chunxiao
  • Zhang, Jie
  • Chen, Yiming
  • Feng, Yujing
  • Yang, Aimin

Abstract

This paper presents a new numerical method to solve the constitutive equations of fractional-order viscoelastic Euler–Bernoulli beams. Firstly, the constitutive equation of Euler–Bernoulli beams is established by analyzing the constitutive relation between the fractional viscoelastic materials. Secondly, the constitutive equation of the beams is transformed into a matrix equation by skillfully using a Quasi-Legendre polynomial in the time domain, which can greatly simplify the solution process. Then the matrix equation is discretized and solved, and the numerical solutions are obtained. Finally, dynamic analysis of two different fractional viscoelastic materials is carried out by numerical experiments, and the influences of time on displacements are considered for the first time. With the change of time and position, displacements under different external loads are obtained for the polybutadiene beams and butyl B252 beams, and the change law of displacements is found. In addition, the performances of the two materials are compared and analyzed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:128:y:2019:i:c:p:275-279
    DOI: 10.1016/j.chaos.2019.07.035
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    Cited by:

    1. 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).
    2. Li, Qing & Chen, Huanzhen, 2022. "Numerical analysis for compact difference scheme of fractional viscoelastic beam vibration models," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    3. Li, Yiqun & Wang, Hong, 2023. "A finite element approximation to a viscoelastic Euler–Bernoulli beam with internal damping," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 138-158.
    4. Muñoz-Vázquez, Aldo Jonathan & Sánchez-Torres, Juan Diego & Defoort, Michael & Boulaaras, Salah, 2021. "Predefined-time convergence in fractional-order systems," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    5. 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.
    6. Dang, Rongqi & Chen, Yiming, 2021. "Fractional modelling and numerical simulations of variable-section viscoelastic arches," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    7. 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).
    8. Tabatabaei, S. Sepehr & Dehghan, Mohammad Reza & Talebi, Heidar Ali, 2022. "Real-time prediction of soft tissue deformation; a non-integer order modeling scheme and a practical verification for the theoretical concept," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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