基于时域谱单元的功能梯度材料结构波传播分析

徐超,王腾

振动与冲击 ›› 2015, Vol. 34 ›› Issue (13) : 18-23.

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PDF(1549 KB)
振动与冲击 ›› 2015, Vol. 34 ›› Issue (13) : 18-23.
论文

基于时域谱单元的功能梯度材料结构波传播分析

  • 徐超,王腾
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Wave Propagation Analysis of Functionally Graded Material Structures Using Time-Domain Spectral Element

  • XU Chao WANG Teng
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摘要

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。

Abstract

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 by the uniformed model, layer-wise model and continuous material model, respectively. Wave dynamic response in functionally graded structure under a central impact load was studied. The proposed element was verified through comparisons to the analytical solution of reference literature. Characteristics of high-frequency guided wave propagation in planar functionally graded material structures were investigated. Numerical Results demonstrate that uniformed model fails to describe the wave field behavior in the graded material structure. There are obvious differences about Amplitude of wave response, phase and phase velocity calculated by layer-wise model and continuous model. Continuous model can simulate the spatially variation of material property better. Symmetry longitudinal wave and asymmetry transverse wave doesn’t disperse obviously, while symmetry transverse wave disperse obviously.   

关键词

功能梯度材料 / 弹性波 / 谱单元 / 时域响应

Key words

 functionally graded material, elastic wave, spectral element, time-domain response  /

引用本文

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徐超,王腾. 基于时域谱单元的功能梯度材料结构波传播分析[J]. 振动与冲击, 2015, 34(13): 18-23
XU Chao WANG Teng . Wave Propagation Analysis of Functionally Graded Material Structures Using Time-Domain Spectral Element[J]. Journal of Vibration and Shock, 2015, 34(13): 18-23

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