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

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

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 200, issue C, 361-376

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.

Keywords: Euler–Bernoulli beam; Variable order fractional model; Collocation method; Shifted Bernstein function; Shifted Legendre polynomial; Dynamic behavior (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:200:y:2022:i:c:p:361-376

DOI: 10.1016/j.matcom.2022.04.035

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