Scattering of SH-wave by a circular cavity in radial inhomogeneous piezoelectric medium
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摘要: 利用复变函数理论对SH波作用下含圆孔径向非均匀压电介质的反平面动力特性进行了研究。压电介质的密度沿径向按幂函数形式变化，但压电参数、弹性参数、介电参数均为常数。利用变量替换法将非均匀压电介质的变系数波动方程组转化为标准的Helmholtz方程组，得到了满足边界条件的波函数解析表达式。通过数值算例分析了入射角度、入射波频率、幂次等对应力集中系数和电场强度集中系数的影响，并与已有文献进行比较。结果表明，某些参数组合下，动应力集中系数与电场强度集中系数均随幂次增大而增大。Abstract: The dynamic anti-plane behavior of the radial inhomogeneous piezoelectric medium with a circular cavity under the SH-wave was investigated using the complex function theory. It was assumed that the density of the piezoelectric medium varied as a power-law function on the radial distance but the elastic parameters, the piezoelectric parameters, and the dielectric parameters all remained as constants. The wave equations of the inhomogeneous piezoelectric medium were converted to the standard Helmholtz equations by variable substitution and the analytical expression of the wave function satisfying the boundary condition was obtained. The influence of the incident angle, the frequency of incident wave and the power of the power-law function, etc. on the dynamic stress concentration factor and electric field intensity concentration factor was analyzed and compared with the existing references in the calculated example. The numerical results show that the values of the dynamic stress concentration factor and the electric field intensity concentration factor increase as the power increases with combination of certain parameters.
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图 1 含圆孔径向非均匀压电介质模型
Figure 1. Model of the radial inhomogeneous piezoelectric medium with a circular cavity
图 3 SH波入射角度不同时动应力集中系数的变化
Figure 3. Varition of DSCF around the circular cavity edge by SH-wave with different incident angles
图 4 SH波水平入射时圆孔周边动应力集中系数随波数ka的变化情况
Figure 4. DSCF around circular cavity edge vs.ka by horizontal SH-wave
图 5 SH波垂直入射时圆孔周边动应力集中系数随波数ka的变化情况
Figure 5. DSCF around circular cavity edgevs.ka by vertical SH-wave
图 6 SH波水平入射时圆孔周边动应力集中系数随λ变化情况
Figure 6. DSCF around circular cavity edge vs. λ 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幂次β的变化情况
Figure 7. DSCF around circular cavity edge vs. β by horizontal SH-wave
图 8 SH波垂直入射时圆孔θ=π/2处动应力集中系数随ka的变化
Figure 8. DSCF around circular cavity edge vs. ka by vertical SH-wave
图 9 SH波以不同角度入射时圆孔周边电场强度系数的变化情况
Figure 9. Variation of EFICF around circular cavity edge by SH-wave with different incident angles
图 10 SH波水平入射时圆孔周边电场强度系数随λ的变化情况
Figure 10. EFICF around circular cavity edge vs. λ by horizontal SH-wave
图 11 SH波水平入射时圆孔周边电场强度系数随β变化情况
Figure 11. EFICF around circular cavity edge vs. β by horizontal SH-wave
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