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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[1] Li X F, Peng X L, Lee K Y.The static response of functionally graded radially polarized piezoelectric spherical shells as sensors and actuators[J].Smart Materials and Structures, 2010, 19(19):035010. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=beb75ccda9e9622eb7648769914a79fb [2] 时朋朋, 霍华颂, 李星.功能梯度压电/压磁双材料的周期界面裂纹问题[J].力学季刊, 2013, 34(2):191-198. doi: 10.3969/j.issn.0254-0053.2013.02.003Shi Pengpeng, Huo Huasong, Li Xing.Periodic interfacial cracks in a functionally graded piezoelectric/piezomagnetic bimaterials[J].Chinese Quarterly of Mechanics, 2013, 34(2):191-198. doi: 10.3969/j.issn.0254-0053.2013.02.003 [3] 靳静, 马鹏.压电压磁双层材料界面裂纹断裂特性进一步分析[J].工程力学, 2013, 30(6):327-333. http://kns.cnki.net/KCMS/detail/detail.aspx?filename=GCLX201306049&dbname=CJFD&dbcode=CJFQJin Jing, Ma Peng.Further analysis for fracture behaviors of an interfacial crack between piezoelectric and piezomagnetic layers[J].Engineering Mechanics, 2013, 30(6):327-333. http://kns.cnki.net/KCMS/detail/detail.aspx?filename=GCLX201306049&dbname=CJFD&dbcode=CJFQ [4] 舒小平.球壳与柱壳之功能梯度压电涂层的热效应分析[J].中国机械工程, 2011, 22(24):2993-3000. http://d.old.wanfangdata.com.cn/Periodical/zgjxgc201124022Shu Xiaoping.Thermal response of functionally graded piezoelectric coatings on sphere and cylinder shells[J].China Mechanical Engineering, 2011, 22(24):2993-3000. http://d.old.wanfangdata.com.cn/Periodical/zgjxgc201124022 [5] 舒小平.正交压电复合材料层板各类边界的解析解[J].工程力学, 2013, 30(10):288-295. http://www.cnki.com.cn/Article/CJFDTotal-GCLX201310042.htmShu Xiaoping.Analytical solutions of cross-ply piezoelectric composite laminates with various boundary conditions[J].Engineering Mechanics, 2013, 30(10):288-295. http://www.cnki.com.cn/Article/CJFDTotal-GCLX201310042.htm [6] Hassan A, Song T S.Dynamic anti-plane analysis for two symmetrically interfacial cracks near circular cavity in piezoelectric bi-materials[J].Applied Mathematics and Mechanics, 2014, 35(10):1261-1270. doi: 10.1007/s10483-014-1891-9 [7] 宋天舒, 刘殿魁, 于新华.SH波在压电材料中的散射和动应力集中[J].哈尔滨工程大学学报, 2002, 23(1):120-123. doi: 10.3969/j.issn.1006-7043.2002.01.025Song Tianshu, Liu Diankui, Yu Xinhua.Scattering of SH-wave and dynamic stress concentration in a piezoelectric medium with a circular hole[J].Journal of Harbin Engineering University, 2002, 23(1):120-123. doi: 10.3969/j.issn.1006-7043.2002.01.025 [8] 杨在林, 黑宝平, 杨钦友.径向非均匀介质中圆形夹杂的动应力分析[J].力学学报, 2015, 47(3):539-543. http://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201503019.htmYang Zailin, Hei Baoping, Yang Qinyou.Dynamic analysis on a circular inclusion in a radially inhomogeneous medium[J].Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(3):539-543. http://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201503019.htm [9] 齐辉, 杨杰.SH波入射双相介质半空间浅埋任意位置圆形夹杂的动力分析[J].工程力学, 2012, 29(7):320-327. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK201203519580Qi Hui, Yang Jie.Dynamic analysis for shallowly buried circular inclusions of arbitrary positions impacted by SH-wave in bi-material half space[J].Engineering Mechanics, 2012, 29(7):320-327. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK201203519580 [10] 林宏, 刘殿魁.半无限空间中圆形孔洞周围SH波的散射[J].地震工程与工程振动, 2002, 22(2):9-16. doi: 10.3969/j.issn.1000-1301.2002.02.002Lin Hong, Liu Diankui.Scattering of SH-wave around a circular cavity in half space[J].Earthquake Engineering and Engineering Vibration, 2002, 22(2):9-16. doi: 10.3969/j.issn.1000-1301.2002.02.002 [11] 丁晓浩, 齐辉, 赵元博.含有直线裂纹的直角域中椭圆形夹杂对SH波的散射[J].天津大学学报, 2016, 49(4):415-421. http://d.old.wanfangdata.com.cn/Periodical/tianjdxxb201604012Ding Xiaohao, Qi Hui, Zhao Yuanbo.Scattering of SH-wave by elliptic inclusion in right-angle plane with beeline crack[J].Journal of Tianjin University, 2016, 49(4):415-421. http://d.old.wanfangdata.com.cn/Periodical/tianjdxxb201604012 [12] 李冬, 宋天舒.含圆孔直角域压电介质的动力反平面特性[J].哈尔滨工程大学学报, 2010, 31(12):1606-1612. doi: 10.3969/j.issn.1006-7043.2010.12.008Li Dong, Song Tianshu.Dynamic anti-plane behavior for a quarter-infinite piezoelectric medium with a subsurface circular cavity[J].Journal of Harbin Engineering University, 2010, 31(12):1606-1612. doi: 10.3969/j.issn.1006-7043.2010.12.008 -
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