Scattering of SH-wave by a circular cavity near the vertical boundary in the piezoelectric bi-material half-space
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摘要: 利用“Green函数法”和“镜像法”对垂直边界附近含圆孔的半空间双相压电介质对SH波的散射问题进行分析，得到其稳态解。利用镜像法得到满足水平边界应力自由与电位移自由的波函数解析表达式。根据垂直边界连续性条件，利用“契合法”建立第一类Fredholm型积分方程组，得到圆孔周边的动应力集中系数与电场强度集中系数解析表达式。数值算例分析了入射波频率、入射角度、介质参数等对动应力集中系数与电场强度集中系数的影响，并与已有文献进行比较。计算表明，高频SH波垂直入射危害较大。Abstract: The scattering of the SH-wave by a circular cavity near the vertical boundary in the piezoelectric bi-material half-space was analyzed using the Green function method and the mirror method to obtain the steady state response. The analytical expression of the wave function was obtained on the horizontal boundaries using the mirror method. This function was the stress-free and electric-displacement-free. According to the continuity condition on the vertical boundary, the first kind of Fredholm integral equations were established, thereby obtaining the analytical expression of the dynamic stress concentration factor and the electric field intensity concentration factor around the edge of the circular cavity by the conjunction method. The influence of the frequencies of the incident wave, the incident angle and the media parameter, etc., on the dynamic stress concentration factor and the electric field intensity concentration factor was examined and compared with existing literatures using calculating examples. The numerical results show that serious damage occurs when the high-frequency incident SH wave comes in vertically.
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图 1 含圆孔的半空间双相压电介质模型
Figure 1. Model of a piezoelectric bi-material in half space with a circular cavity
图 3 含圆孔的半空间双相压电介质垂直界面的契合
Figure 3. Conjunction of piezoelectric bi-material vertical interface in half space with a circular cavity
图 5 SH波水平入射时圆孔周边动应力集中系数随λⅠ的分布
Figure 5. DSCF around circular cavity edge vs. λⅠ by horizontal SH-wave
图 6 SH波水平入射时圆孔周边动应力集中系数随参数ka的分布
Figure 6. DSCF around circular cavity edge vs. ka by horizontal SH-wave
图 7 SH波水平入射时圆孔周边动应力集中系数随λⅠ的分布
Figure 7. DSCF around circular cavity edge vs. λⅠ by horizontal SH-wave
图 8 SH波水平入射时圆孔周边动应力集中系数随λⅡ的分布
Figure 8. DSCF around circular cavity edge vs. λⅡ by horizontal SH-wave
图 9 SH波水平入射时圆孔周边应力集中系数随参数ka的变化
Figure 9. DSCF around circular cavity edge vs. ka by horizontal SH-wave
图 10 SH波以不同角度入射时圆孔周边电场强度集中系数的分布
Figure 10. EFICF around circular cavity edge by SH-wave with different incident angles
图 11 SH波水平入射时圆孔周边电场强度集中系数随参数ka的分布
Figure 11. EFICF around circular cavity edge vs.ka by horizontal SH-wave
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