SH波入射下正交各向异性双相介质界面附近圆孔的动应力集中

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (1) : 301-307.

论文

兰国冠1，张村峰1，许华南1，张剑伟2

作者信息 +

Dynamic stress concentration of a circular cavity near the interface of orthotropic bimaterials under SH wave incidence

LAN Guoguan 1, ZHANG Cunfeng1, XU Huanan1, ZHANG Jianwei2

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文章历史 +

摘要

基于复变函数和格林函数的方法，探讨了SH波在具有圆孔的正交各向异性两相介质中的散射，分析了圆孔周围的动态响应规律。首先建立问题的二维解析模型，将全空间分为两个部分：均匀各向同性上半空间以及含圆柱形孔洞的正交各向异性下半空间。采用格林函数法推导出了两半空间界面处各点的格林函数表达式，并引入复变量，构造出了SH波入射下求解区域内位移和应力的表达式。考虑界面的连续性条件，将未定反平面力加载到两个半空间的水平界面上，推导出Fredholm定解积分方程组，用弱奇异积分方程的直接离散方法求解。最终通过算例分析，发现介质的正交各向异性参数、入射波波数、角度以及孔洞埋深等对下半空间圆孔周边的动应力集中系数(DSCF) 影响显著。
关键词：SH波；Green函数；各向异性双相介质界面；圆孔；DSCF

Abstract

Based on the complex function method and Green's function, the scattering of SH wave in orthotropic bimaterials with a circular cavity iwas discussed, and the dynamic response around the cavity iwas analyzed. Firstly, the two-dimensional analytical model of the problem iwas established, and the whole space iwas divided into two parts: the homogeneous isotropic upper half space and the orthotropic lower half space with a cylindrical cavity. Using Green's function method, the Green’s function expression of each point at the interface of two half spaces iwas derived, and the complex variable iwas introduced to construct the wave field expression for solving the displacement and stress in the region under the incidence of SH wave. Considering the continuity condition of the interface, the undetermined anti-plane force iwas loaded on the horizontal interface of two half spaces, and then the Fredholm definite solution integral equations awere derived and solved by the direct discretization method of weak singular integral equations. Finally, through the calculation and analysis of examplesthrough a series of calculating analysis, it iwas found that the orthotropic parameters of the medium, the number of incident waves, the angle and the buried depth of the cavity have significant effects on the dynamic stress concentration factor (DSCF) around the circular cavity in the lower half space.
Key words: SH-waves; Green’s function; anisotropic bimaterials interface; circular cavity; DSCF

导出引用

兰国冠1，张村峰1，许华南1，张剑伟2 . SH波入射下正交各向异性双相介质界面附近圆孔的动应力集中[J]. 振动与冲击, 2023, 42(1): 301-307

LAN Guoguan 1, ZHANG Cunfeng1, XU Huanan1, ZHANG Jianwei2. Dynamic stress concentration of a circular cavity near the interface of orthotropic bimaterials under SH wave incidence[J]. Journal of Vibration and Shock, 2023, 42(1): 301-307

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