Fractional modelling and numerical simulations of variable-section viscoelastic arches - Dang, Rongqi; Chen, Yiming (Applied mathematics and computation, 2021)
•The fractional governing equations of three variable section viscoelastic arches are established based on two fractional viscoelastic constitutive models.•Numerical solutions of displacement, stress and strain are obtained directly in the time domain by shifted Chebyshev polynomial algorithm.•Convergence analysis and error estimation prove the high accuracy and efficiency of proposed algorithm.•Performance testing for variable-section arches with different viscoelastic materials. In this paper, two fractional viscoelastic constitutive models are used to establish nonlinear fractional integro-differential governing equations of variable-section viscoelastic arches. Shifted Chebyshev polynomial algorithm is introduced to numerically solve the governing equations directly in time domain. The feasibility and accuracy of the proposed algorithm are verified by convergence analysis and error estimation of a mathematical example. In addition, the dynamic responses of variable-section viscoelastic arches with three materials under two fractional models are also studied to verify the effectiveness of shifted Chebyshev polynomial algorithm.