摘要
利用复变函数和Green函数法研究了垂直半空间中双相介质界面附近圆孔对SH波的散射与动应力集中问题。该问题的解答采用镜像法,首先构造出含有圆孔的直角平面区域出平面问题的Green函数,然后利用"契合"技术,并根据界面处位移连续性条件将解答归结为具有弱奇异性的第一类Fredholm积分方程组的求解,结合散射波的衰减特性,直接离散该方程组,把积分方程组转化为线性代数方程组可得到该问题的数值结果。最后,通过算例分析了圆孔的动应力集中情况。结果表明,与全空间中界面附近圆孔对SH波的散射相比,由于垂直半空间自由边界的存在,孔边动应力集中系数明显增大;另外,入射波由硬介质(波速大)进入到软介质(波速小)时,与均匀介质相比,孔边动应力集中更显著,最不利的参数组合,孔边动应力集中系数几乎提高了一倍,入射波由软介质进入到硬介质时,情况相反。
The scattering of SH-wave by the circular cavity near the bimaterial interface in a vertical half-space and dynamic stress concentration were explored based on the complex function method and the Green＇s function method. The solution of the present problem was given by the image method. Firstly, a suitable Green＇s function was constructed, which was the essential solution of displacement field for an elastic right-angle plane with a circular cavity subjected to anti-plane harmonic line source loading at the horizontal surface. Secondly, the conjunction method was used to develop the scattering model of SH-wave, then a series of Fredholm integral equations of the first kind for determining the unknown forces were established through the continuity conditions expressed in terms of the Green＇s function. Finally, the dynamic stress concentration was analyzed by numerical examples. The numerical examples show that the dynamic stress concentration depends on the incident frequency and angle of SH-wave, the geometrical position of the circular cavity, and the different media combination parameters. Compared with the scattering of SH-wave by the circular cavity in a complete space, the free boundary of the vertical half-space has great effect on the incident plane SH-wave and the dynamic stress concentration factors around the circular cavity are magnified obviously while the SH-wave disturbs from a rigid medium to a soft medium.
出处
《爆炸与冲击》
EI
CAS
CSCD
北大核心
2009年第1期73-79,共7页
Explosion and Shock Waves
基金
黑龙江自然科学基金项目(A0206)
关键词
固体力学
动应力集中
GREEN函数
SH波散射
垂直半空间
双相介质界面
圆孔
solid mechanics
dynamic stress concentration
Green＇ s function
scattering of SH-wave vertical half-space
bimaterial interface
circular cavity
