纳米圆形孔洞SH波散射的复变函数解答  

Complex variable function solution for SH wave scattering in nano circular hole

作　　者：吴红梅[1,2] 欧志英 Wu Hongmei;Ou Zhiying(School of Science,Lanzhou University of Technology,730050,Lanzhou,China;School of Mechanical and Electronical Engineering,Lanzhou University of Technology,730050,Lanzhou,China)

机构地区：[1]兰州理工大学理学院,兰州730050 [2]兰州理工大学机电工程学院,兰州730050

出　　处：《应用力学学报》2021年第2期763-769,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11362009;11862014)。

摘　　要：利用复变函数理论,研究了平面内纳米圆形孔洞对剪切波(SH波)的散射问题。首先给出宏观尺度下平面内嵌有孔洞的入射波场和散射波场。其次考虑表面效应,给出纳米尺度下的边界条件,建立求解散射波函数中含有未知系数的无穷代数方程组,并利用三角函数的正交性得出了应力场的解析解。最后通过算例分析了表面效应、量纲为一的波数对孔洞周围动应力集中因子及径向应力的影响,结果表明:表面效应减弱了孔洞周围的动应力集中,但增强了对径向应力的影响,随着表面效应的增大,动应力集中因子单调递减而径向应力单调递增。随着量纲为一的波数的增大,应力集中因子减小,而径向应力在不同区间内的变化趋势不同。The scattering of shear waves(SH waves)by nano-circular hole in plane is studied by using complex function theory.Firstly,the incident wave field and the scattered wave field are presented.Secondly,considering the surface effect,the boundary condition is given,and the infinite algebraic equations are established to solve the unknown coefficients of the scattering wave function.By using the orthogonality of trigonometric function,the analytic solution of stress field is obtained.Finally,the influence of surface effect and non dimensional wave number on the dynamic stress concentration factor and the radial stress around the hole are analyzed by some examples,the numerical results show that the surface effect weakens the dynamic stress concentration but enhances the radial stress around the hole.With the increases of wave number,the stress concentration factor decreases and the variation trend of radial stress is different in different intervals.

关 键 词：SH波的散射 复变函数理论 表面效应 正交性 动应力集中因子 径向应力 

分 类 号：O343[理学—固体力学]