Shifted-Chebyshev-polynomial-based numerical algorithm for fractional order polymer visco-elastic rotating beam

In this paper, an effective numerical algorithm is proposed for the first time to solve the fractional visco-elastic rotating beam in the time domain. On the basis of fractional derivative Kelvin–Voigt and fractional derivative element constitutive models, the two governing equations of fractional v...

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Bibliographic Details
Published in:Chaos, solitons and fractals Vol. 132; p. 109585
Main Authors: Wang, Lei, Chen, Yi-Ming
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.03.2020
Elsevier
Subjects:
Approximation technique
Fractional governing equation
Fractional visco-elastic rotating beam
Mathematics
Numerical solution
Operator matrix
Shifted Chebyshev polynomials
Fractional visco-elastic rotating beam
Fractional governing equation
Approximation technique
Operator matrix
Numerical solution
Shifted Chebyshev polynomials
ISSN:0960-0779, 1873-2887
Online Access:Get full text
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Summary:In this paper, an effective numerical algorithm is proposed for the first time to solve the fractional visco-elastic rotating beam in the time domain. On the basis of fractional derivative Kelvin–Voigt and fractional derivative element constitutive models, the two governing equations of fractional visco-elastic rotating beams are established. According to the approximation technique of shifted Chebyshev polynomials, the integer and fractional differential operator matrices of polynomials are derived. By means of the collocation method and matrix technique, the operator matrices of governing equations can be transformed into the algebraic equations. In addition, the convergence analysis is performed. In particular, unlike the existing results, we can get the displacement and the stress numerical solution of the governing equation directly in the time domain. Finally, the sensitivity of the algorithm is verified by numerical examples.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2019.109585