Wave propagation analysis for functionally graded material structures using time-domain spectral element method

A new arbitrary quadrangular Gauss-Lobatto-Legendre time-domain spectral element was established considering spatially continuous variation of material property of functionally graded material structures in the macroscopic sense. The variation of material property was modeled with the uniformed model, the layer-wise model and the continuous material model, respectively. Wave dynamic response of a 2-D functionally graded structure under a central impact load was studied. The effectiveness of the proposed element method was verified through comparing the numerical simulation results with the proposed element method with the analytical solution in reference literature. Characteristics of high-frequency guided wave propagation in planar functionally graded material structures were investigated. Numerical results demonstrated that the uniformed model fails to describe the wave field behavior of functionally graded material structures; there are obvious differences between amplitude of wave response, phase and phase velocity calculated with the layer-wise model and the continuous model, respectively; the continuous model can be used to simulate the spatially variation of the material property better; the phase velocity dispersion of the symmetric longitudinal wave and asymmetric transverse wave is not obvious, while that of the symmetric transverse wave is obvious.