A Numerical Method for Simulating Viscoelastic Plates Based on Fractional Order Model

Abstract

In this study, an efficacious method for solving viscoelastic dynamic plates in the time domain is proposed for the first time. The differential operator matrices of different orders of Bernstein polynomials algorithm are adopted to approximate the ternary displacement function. The approximate results are simulated by code. In addition, it is proved that the proposed method is feasible and effective through error analysis and mathematical examples. Finally, the effects of external load, side length of plate, thickness of plate and boundary condition on the dynamic response of square plate are studied. The numerical results illustrate that displacement and stress of the plate change with the change of various parameters. It is further verified that the Bernstein polynomials algorithm can be used as a powerful tool for numerical solution and dynamic analysis of viscoelastic plates.

Dynamic analysis of viscoelastic foundation plate with fractional Kelvin–Voigt model using shifted Bernstein polynomials

“…Vibration of the plate with respect to the damping factor is discussed. Jin et al [4] studied the dynamics of viscoelastic plates using Bernstein polynomial algorithm. The influence of extrinsic load, plate side length, plate thickening, and boundary conditions on the dynamic response of square plates are studied.…”

High-Order Schemes for Nonlinear Fractional Differential Equations

“…Low-order approaches are the most frequently employed methods for FDEs, and it has been proven to be difficult to construct high-order and adaptive schemes [13,15,21,22]. In this paper, we present high-order computational schemes for solving nonlinear FDEs.…”