Numerical analysis of variable fractional viscoelastic column based on two-dimensional Legendre wavelets algorithm

In this paper, two-dimensional Legendre wavelets algorithm is applied for the first time to solve a variable order fractional partial differential governing equation of viscoelastic column in the time domain. Firstly, the governing equation of a viscoelastic column is established according to a variable order fractional constitutive model. Secondly, the unknown function is expanded into the elements of two-dimensional Legendre wavelets. In order to obtain the numerical solutions of this type of equation, the differential operator matrices based on Legendre wavelets of integer order and variable order fractional are derived. The operator matrices are used to convert the initial governing equation into algebraic equations that are easy to solve in the time domain. The efficiency and accuracy of the algorithm are verified through the convergence analysis of Legendre wavelets and the error estimations of numerical example. Finally, the displacement solutions of the viscoelastic column under constant load and variable load are considered, and the columns with different cross-section shapes are studied. The results show that the proposed numerical algorithm is efficient in dynamic analysis of viscoelastic columns. (c) 2021 Elsevier Ltd. All rights reserved.