IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v200y2022icp361-376.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847542200177X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.04.035?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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).
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. 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.
    3. 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).
    4. 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).
    5. 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).
    6. 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).
    7. Li, Hang & Shen, Yongjun & Han, Yanjun & Dong, Jinlu & Li, Jian, 2023. "Determining Lyapunov exponents of fractional-order systems: A general method based on memory principle," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    8. Li, Jin & Su, Xiaoning & Zhao, Kaiyan, 2023. "Barycentric interpolation collocation algorithm to solve fractional differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 340-367.
    9. Mohamed Kharrat & Hassen Arfaoui, 2023. "A New Stabled Relaxation Method for Pricing European Options Under the Time-Fractional Vasicek Model," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1745-1763, April.
    10. 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).
    11. Dang, Rongqi & Chen, Yiming, 2021. "Fractional modelling and numerical simulations of variable-section viscoelastic arches," Applied Mathematics and Computation, Elsevier, vol. 409(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:200:y:2022:i:c:p:361-376. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.