基于时域谱单元的功能梯度材料结构波传播分析

摘要

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.%考虑功能梯度材料结构宏观材料属性的连续空间变化，推导了一种任意四边形形状的 Gauss －Lobatto －Legendre 时域谱单元。分别采用均匀化模型、分层离散模型和连续材料模型三种建模方法描述材料的梯度变化特性。研究了二维功能梯度结构在中心冲击载荷下的波动力学响应，将数值模拟结果与文献理论解进行了对比，验证了单元的有效性，研究了高频导波在二维功能梯度材料结构中的传播特性。计算结果表明：均匀化模型无法准确描述功能梯度材料结构中的波场行为；采用分层离散模型计算的波响应幅值、相位和相速度均与采用连续材料模型计算的结果有差异，采用连续材料模型能更好模拟功能材料宏观材料性质空间连续变化的特征。功能梯度材料中对称模式纵波、反对称模式横波的相速度频散现象不明显，对称模式横波的相速度频散明显。