半无限功能梯度材料结构中圆孔对弹性波的多重散射

MULTIPLE SCATTERING OF ELASTIC WAVES IN SEMI-INFINITE FUNCTIONALLY GRADED MATERIAL WITH A CIRCULAR CAVITY

基于弹性波多体散射理论,采用波函数展开法,研究了半无限指数梯度材料中圆孔对弹性波的多重散射和动应力集中,得到了问题的解析解,给出了圆孔动应力集中系数的数值解,分析了圆孔与边界的距离、入射波波数以及材料的非均匀参数对圆孔周围动应力集中系数的影响。分析表明:梯度材料的非均匀参数小于零时对最大动应力影响较小,但是对动应力在圆周的分布有较大影响;大于零时对最大动应力和动应力在圆周的分布影响都很大,特别是在圆孔与边界的距离较小时影响更大。

Based on the multiple scattering theory of elastic waves, employing the wave ftmction expansion method, the multiple scattering and the dynamic stress in semi-infinite functionally graded material with a circular cavity are investigated. The analytical solution of the problem is derived, and the numerical solution of the dynamic stress concentration factors around the cavity is presented. The effects of the distance between the cavity and the edge of the structure, the wave number and the heterogeneous parameter of materials on the dynamic stress concentration factors are analyzed. Analysis has shown that when the heterogeneous parameter of materials is less than zero, it has less influence on the maximum dynamic stress around the cavity; however, it has greater influence on the distribution of dynamic stress around the cavity. When the heterogeneous parameter of materials is greater than zero, it has greater influence on both the maximum dynamic stress and the distribution of it around the cavity, especially in the case when the distance between the cavity and the edge is comparatively small.