SH波对浅埋圆形弹性夹杂附近任意三角形凸起地形的散射

Scattering of SH Waves by a Scalene Triangular Hill near Subsurface Elastic Cylindrical Inclusion

利用"契合"的思想,给出了地下弹性夹杂与地面任意三角形凸起地形对SH波散射问题的解析解答。将整个求解区域分割成三部分,区域Ⅰ为带有半圆形弧底的三角形凸起,区域Ⅱ为含半圆形凹陷和浅埋孔洞的弹性半空间,区域Ⅲ为一圆柱形弹性体。在区域Ⅰ中构造满足三角形两斜边应力自由的驻波函数,在区域Ⅱ中构造出半圆形凹陷和浅埋孔洞的散射波,在区域Ⅲ内构造一驻波函数,使得圆柱边界应力不受约束;利用复平面下坐标移动,通过区域Ⅰ和区域Ⅱ以及区域Ⅱ和区域Ⅲ的两个"公共边界"位移应力连续条件,建立起求解该问题的无穷代数方程组,并截断有限项进行求解,最后通过具体算例及结果分析得出相应结论。

The scatting of SH waves by a scalene triangular hill above a subsurface elastic cylindrical inclusion is investigated following the conjunction' thought.the solution domain is divided into three parts,domainⅠ involves a scalene triangular hill with hemi-circular bottom,domain Ⅱ is a half space with a hemi-circular canyon and a subsurface cavity,domain Ⅲ remains an elastic cylinder.A standing wave function is constructed in domainⅠsatisfying and the zero-stress condition at the triangular wedges.In domain Ⅱ,two scattering wave functions satisfying the condition of stress-free at the horizontal surface are established.In domain Ⅲ,another standing wave function is constructed to meet the random-stress requirement at the circle interface.A infinite set equations are solved to draw the conclusions.