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。
Based on the complex function method and Green's function,the scattering of SH wave in orthotropic bimaterials with a circular cavity was discussed,and the dynamic response around the cavity was analyzed.Firstly,the two-dimensional analytical model of the problem was established,and the whole space was 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 was derived,and the complex variable was 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 was loaded on the horizontal interface of two half spaces,and then the Fredholm definite solution integral equations were derived and solved by the direct discretization method of weak singular integral equations.Finally,through the calculation and analysis of examples,it was 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.
作者
兰国冠
张村峰
许华南
张剑伟
LAN Guoguan;ZHANG Cunfeng;XU Huanan;ZHANG Jianwei(School of Resource Engineering,Longyan University,Longyan 364000,China;School of Safety Engineering,Shenyang Aerospace University,Shenyang 110000,China)
出处
《振动与冲击》
EI
CSCD
北大核心
2023年第1期301-307,共7页
Journal of Vibration and Shock
基金
国家自然科学基金青年项目(12002143)。
