Numerical analysis of fractional viscoelastic column based on shifted Chebyshev wavelet function

Applied Mathematical Modelling, Elsevier, 91, (2021), 374–389

Jiawei Cao 1, Yiming Chen 1,2, Yuanhui Wang 1, Gang Cheng 3, Thierry Barrière 2, Lei Wang 1


1 College of Sciences, Yanshan University, China

2 Department of Applied Mechanics, FEMTO-ST Institute, CNRS/ENSMM/UTBM, Univ. Bourgogne Franche-Comté, Besançon 25000, France

3 INSA Centre Val de Loire, Univ. Tours, Univ. Orléans, LaMé, 41034 Blois, France


An innovative numerical procedure for solving the viscoelastic column problem based on fractional rheological models, directly in the time domain, is investigated. Firstly, the governing equation is established according to the fractional constitutive relation. Secondly, the resulting equation is transformed into algebraic equation and solved by using the shifted Chebyshev wavelet function. Furthermore, the convergence analysis and the retained numerical benchmarks are carried out to validate the performance of the proposed method. A small value of the absolute error between numerical and accurate solution is obtained. Finally, the dynamic analysis of viscoelastic beam-column problems is investigated with different cross-section shape (circular and square) under various loading conditions (axial compressive force and harmonic load). The displacement, strain and stress of the viscoelastic column at different time and position are determined. The deformation and stress of the viscoelastic column of different materials under the same loading condition are compared. The results in the paper show the highly accuracy and efficiency of the proposed numerical algorithm in the dynamical stability analysis of the viscoelastic column.


Fractional constitutive model
Viscoelastic column
Shifted Chebyshev wavelet function
Convergence analysis
Numerical solution
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