无限大功能梯度板中弹性导波频散特性的研究

玻璃钢/复合材料 ›› 2019, Vol. 0 ›› Issue (10): 51-57.

无限大功能梯度板中弹性导波频散特性的研究

廖智麒, 罗毅^*

华南理工大学土木与交通学院,广州510641

收稿日期:2018-12-19 出版日期:2019-10-28 发布日期:2019-10-28
通讯作者: 罗毅(1968-),男,博士,教授,主要从事材料的疲劳损伤及可靠性方面的研究,debulo@scut.edu.cn。
作者简介:廖智麒(1994-),男,硕士研究生,主要从事复合材料无损检测方面的研究。

STUDY ON DISPERSION CHARACTERISTICS OF ELASTIC GUIDED WAVESIN AN INFINITE FUNCTIONALLY GRADED PLATE

LIAO Zhi-qi, LUO Yi^*

School of Civil Engineering and Transportation, South China University of Technology,Guangzhou 510641, China

Received:2018-12-19 Online:2019-10-28 Published:2019-10-28

摘要/Abstract

摘要： 建立了无限大功能梯度板的理论模型,得到了直角坐标系下功能梯度板的几何方程。采用Rayleigh-Ritz法(RRM),引入Legendre正交多项式作为位移试函数,基于Hamilton原理获得了功能梯度板中弹性导波的频散方程。数值计算各向异性材料组成的无限大功能梯度板中相速度和群速度频散曲线,分析了不同体积分数指数N、不同入射角θ对功能梯度板中导波传播的影响。研究结果表明,当采用高阶节点数计算时,Rayleigh-Ritz法在分析导波问题上具有很好的收敛性和准确性。

关键词: 功能梯度板, 频散曲线, Rayleigh-Ritz法(RRM), Legendre正交多项式, 各向异性

Abstract: In order to investigate the dispersion characteristics of elastic guided waves in an infinite functionally graded plate, this article built the theoretical analysis model for elastic guided waves of a functionally graded plate, and established the geometric equation under Cartesian coordinate system. In this paper, the Legendre orthogonal polynomial is introduced as trial functions of displacement. According to the Hamilton principle, Raleigh-Ritz Method (RRM) is applied to obtain the dispersion equation of elastic guided waves in a functionally graded plate. It is found that Raleigh-Ritz method has a great convergence and accuracy in solving guided wave propagation problems when using high-order node numbers for calculation. Raleigh-Ritz Method is not limited to homogenous plates. Phase velocity and group velocity dispersion curves of an infinite functionally graded plate composed of anisotropic materials are given, and the influences of different volume fraction indexes N and incident angle θ on dispersive behavior for guided wave propagation are analyzed.

Key words: functionally graded plate, dispersion curve, Rayleigh-Ritz method, legendre orthogonal polynomial, anisotropy

中图分类号:

TB332

廖智麒, 罗毅. 无限大功能梯度板中弹性导波频散特性的研究[J]. 玻璃钢/复合材料, 2019, 0(10): 51-57.

LIAO Zhi-qi, LUO Yi. STUDY ON DISPERSION CHARACTERISTICS OF ELASTIC GUIDED WAVESIN AN INFINITE FUNCTIONALLY GRADED PLATE[J]. Fiber Reinforced Plastics/Composites, 2019, 0(10): 51-57.

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