摘要
基于复变函数理论,研究了出平面剪切波在非均匀直角域内的传播特性.介质的非均匀性体现在剪切模量是与空间坐标有关的函数.引入一个位移辅助函数和一对映射函数用以辅助推导控制方程.同时,在复坐标系下可以更方便的进行坐标变换.使用镜像法构造了介质内反射波和散射波的波场表达式.根据圆孔处的边界条件求解了散射波中的未知系数,并给出了直角域空间内波场的解析表达式.在动力学分析中,刚度可以用剪切模量来表示.在算例分析中,讨论了位移幅值和动应力集中系数对非均匀参数,参考波数以及圆孔位置的依赖关系.
Based on the theory of complex variable function,the propagation properties of anti-plane shear wave in inhomogeneous right-angle space are analysed.The inhomogeneity of the medium is reflected in the fact that the shear modulus is a function related to spatial coordinates.A displacement auxiliary function and a pair of mapping functions are introduced to assist in deriving the governing equation.Meanwhile,the transformation between coordinates can be more convenient in the complex coordinate system.The wave field expressions of reflected and scattering waves are constructed by using the image method.The unknown coefficients in the scattering waves are solved according to the boundary condition of the circular hole,and the analytical expressions of the wave field in the right-angle space are given.In dynamic analysis,rigidity can be expressed by shear modulus.In the analysis of numerical examples,the dependence of displacement amplitude and dynamic stress concentration factor(DSCF)on the inhomogeneous parameter,reference wave number,and the position of circular hole are discussed.
作者
卞金来
杨在林
Erasmo Carrera
Jinlai Bian;Zailin Yang;Erasmo Carrera(College of Aerospace and Civil Engineering,Harbin Engineering University,Harbin,150001,China;Key Laboratory of Advanced Material of Ship and Mechanics,Ministry of Industry and Information Technology,Harbin Engineering University,Harbin,150001,China;Department of Mechanical and Aerospace Engineering,Politecnico di Torino,Turin,Italy)
基金
the National Natural Science Foundation of China(Grant No.12072085)
the Natural Science Foundation of Heilongjiang Province of China(Grant No.ZD2021A001)
Research Team Project of Heilongjiang Natural Science Foundation(Grant No.TD2020A001)
the program for Innovative Research Team in China Earthquake Administration.
