Scattering of SH-wave by elliptical inclusion with partial debond curve and circular cavity in half space
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摘要: 采用复变函数法，结合"保角映射"技术及Green函数法，研究SH波作用下半空间内含有部分脱胶的椭圆夹杂以及圆形孔洞的散射问题。首先，利用"保角映射"技术将椭圆夹杂映射为圆夹杂，求出散射波位移场，同时，利用Green函数法与"虚设点源"的方法，求出半空间内椭圆夹杂以及圆孔的位移及应力场；然后，根据椭圆夹杂周围位移、应力连续、圆孔周围应力自由的边界条件，建立无穷线性代数方程组，求解出波函数中的未知系数；最后，在脱胶部分施加大小相等、方向相反的应力，构造出"脱胶模型"，得到半空间内含有部分脱胶的椭圆夹杂以及圆形孔洞的总位移场。数值算例表明，入射角度、入射波频率、缺陷之间的距离、夹杂埋深及脱胶角度等对动应力集中因子有较大影响。Abstract: In order to study the scattering problems of SH-wave by elliptical inclusion with partial debond curve and circular cavity in half space. The method of "conformal mapping" is used to map the elliptical inclusions into circular inclusions. The displacement field and the stress field of the elliptical inclusion and circular cavity are obtained by Green's function method with the ridding of image method. Secondly, infinite system of linear equations are established by boundary conditions, which are continuous around the elliptical inclusion with the displacement and stress, and then the unknown coefficients of wave function are solved by the free around circular cavity with stress. Finally, the "partial debond curve model" is constructed, the equal stress with opposite direction is applied in the partial debond curve. By which we obtain the total displacement field of the elliptical inclusion with a partially debond curve and circular in the half space. Numerical examples show that the dynamic stress concentration factor (DSCF) is influenced by the incident angle, the frequency of incident wave, the distance of the defect, the depth of inclusion and the partial debond curve angle.
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Key words:
- SH wave /
- scattering /
- elliptic inclusion /
- partial debond curve /
- Green's function /
- conformal mapping /
- dynamic stress factor
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图 1 半空间含有部分脱胶的椭圆夹杂及圆形孔洞模型
Figure 1. Model of elliptical inclusion with a partially debond curve and circular cavity in half space
图 2 含椭圆形弹性夹杂及圆孔的半空间作用一出平面线源荷载模型
Figure 2. Half-space model of elliptical inclusion and circular cavity impacted by an out-plane source load
图 3 SH波垂直入射时τθz*随着k1a的分布
Figure 3. Distribution of DSCF with k1a for vertically incident SH wave
图 4 SH波水平入射时τθz*随着θ1*的变化情况
Figure 4. Distribution of DSCF with θ1* for horizontally incident SH wave
图 5 SH波水平入射时随不同角度α在不同入射波频率k1a条件下τθz*的分布
Figure 5. Distribution of DSCF versus the frequency of incident wave at different incident angles for horizontally incident SH wave
图 6 SH波水平入射时τθz*随着k1*的分布
Figure 6. Distribution of DSCF with k1* for horizontally incident SH wave
图 7 SH波水平入射时τθz*随着h/a的变化情
Figure 7. Distribution of DSCF with h/a for horizontally incident SH wave
图 8 SH波水平入射时τθz*随着d/r的变化情况
Figure 8. Distribution of DSCF with d/r for horizontally incident SH wave
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