功能梯度一维六方准晶中裂纹对SH波的散射  

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

作　　者：杨娟 徐燕[1,3] 师金华 丁生虎[1] YANG Juan;XU Yan;SHI Jinhua;DING Shenghu(School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,China;School of Preparatory Education for Nationalities,Ningxia University,Yinchuan 750002,China;Xinhua College,Ningxia University,Yinchuan 750002,China)

机构地区：[1]宁夏大学数学统计学院,银川750021 [2]宁夏大学民族预科教育学院,银川750002 [3]宁夏大学新华学院,银川750002

出　　处：《振动与冲击》2023年第12期249-255,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金(12062022,42064004,12062021);宁夏自然科学基金(2020AAC03061)。

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。Within the framework of the quasicrystal linear dynamic theory,the dynamic fracture of a crack in a functionally graded one-dimensional hexagonal quasicrystal 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 the fracture problem was formulated to two pairs of dual integral equations,which were solved numerically with the 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 show 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 

分 类 号：O346.1[理学—固体力学]