功能梯度一维六方准晶中裂纹对SH波的散射

杨娟1,2,徐燕1,3,师金华2,丁生虎1

振动与冲击 ›› 2023, Vol. 42 ›› Issue (12) : 249-255.

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (12) : 249-255.
论文

功能梯度一维六方准晶中裂纹对SH波的散射

  • 杨娟1,2,徐燕1,3,师金华2,丁生虎1
作者信息 +

Scattering of the SH wave by a crack in functionally graded one dimensional hexagonal piezoelectric quasicrystal

  • YANG Juan1,2,XU Yan1,3,SHI Jinhua2,DING Shenghu1
Author information +
文章历史 +

摘要

在准晶的线性动力学理论框架下,利用积分变换技术研究了功能梯度一维六方准晶在SH波作用下的裂纹动态断裂问题。假设材料性质呈指数函数连续变化。利用Fourier余弦变换,将描述断裂问题的偏微分方程边值问题转化为两对对偶积分方程,采用Copson方法对其进行数值求解。确定了裂纹面上声子场和相位子场显式表达式,得到了动态场强因子。最后通过数值计算主要探究了梯度参数、裂纹长度、振幅、入射角度和标准波数对材料断裂特性的影响规律。此研究为准晶体的优化设计和无损检测奠定了理论基础。

Abstract

Within the framework of quasicrystals linear dynamic theory, the dynamic fracture of a crack in a functionally graded one-dimensional hexagonal quasicrystals subjected to a time-harmonic elastic SH-wave was studied with integral transform technique. The material properties were assumed to vary continuously as an exponential function. Using the Fourier cosine transform, the boundary value problem of partial differential equation describing fracture problem was formulated to two pairs of dual integral equations, which were solved numerically with Copson method. The explicit expressions of phonon and phason elastic fields at crack face were determined and the dynamic stress intensity factors were obtained. Finally, numerical results showed the effects of gradient parameter, crack length , incident angle and normalized wave number on fracture characteristics of material. This study provides a theoretical basis for optimal design and nondestructive testing of quasicrystals.

关键词

SH波 / 准晶 / 梯度 / 裂纹 / 动应力强度因子

Key words

SH wave / quasicrystals / graded / crack / dynamic stress intensity factory

引用本文

导出引用
杨娟1,2,徐燕1,3,师金华2,丁生虎1. 功能梯度一维六方准晶中裂纹对SH波的散射[J]. 振动与冲击, 2023, 42(12): 249-255
YANG Juan1,2,XU Yan1,3,SHI Jinhua2,DING Shenghu1. Scattering of the SH wave by a crack in functionally graded one dimensional hexagonal piezoelectric quasicrystal[J]. Journal of Vibration and Shock, 2023, 42(12): 249-255

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