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

被引：7

作者：

Cui, Yuhuan ^{[1
]}

Qu, Jingguo ^{[1
]}

Han, Cundi ^{[2
]}

Cheng, Gang ^{[3
]}

Zhang, Wei ^{[1
]}

Chen, Yiming ^{[2
,3
]}

机构：

[1] North China Univ Sci & Technol, Coll Sci, Tangshan 063210, Hebei, Peoples R China

[2] Yanshan Univ, Sch Sci, Qinhuangdao 066004, Hebei, Peoples R China

[3] Univ Tours, Univ Orleans, INSA Ctr Val Loire, LaMe, 3 rue chocolaterie, CS 23410, F-41034 Blois, France

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2022年 / 200卷

关键词：

Euler-Bernoulli beam; Variable order fractional model; Collocation method; Shifted Bernstein function; Shifted Legendre polynomial; Dynamic behavior; OPERATIONAL MATRICES; VIBRATION ANALYSIS; NANOBEAMS;

D O I：

10.1016/j.matcom.2022.04.035

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

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. (c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

引用

页码：361 / 376

页数：16

共 21 条

[1] Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein-Legendre Polynomial Collocation Algorithm
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FRACTAL AND FRACTIONAL, 2021, 5 (01) : 1 - 12
[2] Analysis of a fractional viscoelastic Euler-Bernoulli beam and identification of its piecewise continuous polynomial order
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[4] Numerical analysis of fractional-order Euler-Bernoulli beam model under composite model
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[5] Shifted Legendre polynomials algorithm used for the numerical analysis of viscoelastic plate with a fractional order model
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[6] A numerical method for solving fractional-order viscoelastic Euler-Bernoulli beams
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[7] Inverting mechanical and variable-order parameters of the Euler-Bernoulli beam on viscoelastic foundation
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[8] Shifted Bernstein Polynomial-Based Dynamic Analysis for Variable Fractional Order Nonlinear Viscoelastic Bar
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[9] Shifted Legendre Polynomials algorithm used for the dynamic analysis of viscoelastic pipes conveying fluid with variable fractional order model
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[10] Dynamic analysis of variable fractional order cantilever beam based on shifted Legendre polynomials algorithm
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