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

Chaos, Solitons and Fractals, Elsevier, 2020, 132, pp.109585

Lei Wang 1 Yi-Ming Chen 2, 3, 4

1 Nanyang Technological University [Singapour]
2 Department of Information Management
3 PRISME - Laboratoire pluridisciplinaire de recherche en ingénierie des systèmes, mécanique et énergétique
4 LE STUDIUM - LE STUDIUM Loire Valley Institute for advanced studies


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.


Fractional visco-elastic rotating beam
Fractional governing equation
Shifted Chebyshev polynomials
Approximation technique
Operator matrix
Numerical solution
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