Time-domain analysis of fractional-order viscoelastic sandwich plates via shifted Legendre polynomial approach

Abstract

The objective of this study is to investigate the dynamic characteristics of three-dimensional fractional-order viscoelastic sandwich plates. Based on the fractional Kelvin–Voigt constitutive relation, the governing equations involving the spatial variables $(x,y,z)$ and the temporal variable $t$ are derived, and the shifted Legendre polynomial method is introduced for numerical approximation. This method is capable of simultaneously characterizing the mechanical properties of both the elastic and viscoelastic layers, thereby revealing the evolution of the overall displacement field. The key innovations of this work are highlighted as follows: First, a unified time-domain solution for viscoelastic sandwich plates is presented for the first time, achieving integrated modeling and analysis of multi-layer coupled systems. Second, in the numerical examples, a piecewise external load is applied to a three-layer structure. Although the elastic and viscoelastic layers are subjected to different loading conditions, the displacement solutions remain continuous across the interfaces. Moreover, comparison with the exact solution is conducted to validate the error control of the proposed method for complex layered structures. Finally, in practical examples, the differential responses of the elastic and viscoelastic layers under uniform body forces are investigated. The proposed method demonstrates distinct advantages in the dynamic analysis of fractional-order viscoelastic sandwich plates, providing new insights for the numerical simulation and engineering applications of layered composite structures.