含圆孔直角域压电介质的动力反平面特性
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摘要
为了研究直角域附近缺陷对压电材料的动力学行为的影响,利用复变函数法及镜像法研究含界面附近圆孔的直角域压电介质的动应力集中问题,得到了直角域压电介质中圆形孔洞对时间谐和的反平面剪切波散射引起的动应力集中系数和电场强度集中系数的解析表达式,并给出了它们随入射波频率、材料的物理常数和结构几何参数变化的计算结果图.结果表明,在某些参数组合情况下,压电直角域界面附近圆孔边界动应力集中系数的最大值为半无限压电域界面附近圆孔的2～3倍,且电场强度集中系数在低频情况下非常大.对含缺陷直角域压电介质进行动力学分析非常必要.
In order to research the influence of the defect in the vicinity of right-angle space on the dynamic behavior of piezoelectric medium,the dynamic anti-plane behavior for a quarter-infinite piezoelectric medium with a subsurface circular cavity was theoretically investigated.Based on complex variables and mirror imaging methods,the expressions were obtained at the cavity's edge by a dynamic stress concentration factor(DSCF) and an electric field intensity concentration factor(EFICF) which were caused by the scattering of anti-plane shear waves.This scattering satisfied the boundary conditions on both the right-angle surface and the cavity's surface under time-harmonic anti-plane shearing.Some calculating cases were plotted as examples to show the frequencies of incident waves,the medium's parameters,and the structure's geometry influence on the DSCF and EFICF.The calculation results indicate that the maximum number of DSCFs possible in presently used methods is nearly two or three times those on a semi-infinite piezoelectric medium,and the EFICF was more significant at a lower frequency.Dynamic analysis is of importance to a quarter-infinite piezoelectric medium with subsurface defects.
In order to research the influence of the defect in the vicinity of right-angle space on the dynamic behavior of piezoelectric medium,the dynamic anti-plane behavior for a quarter-infinite piezoelectric medium with a subsurface circular cavity was theoretically investigated.Based on complex variables and mirror imaging methods,the expressions were obtained at the cavity's edge by a dynamic stress concentration factor(DSCF) and an electric field intensity concentration factor(EFICF) which were caused by the scattering of anti-plane shear waves.This scattering satisfied the boundary conditions on both the right-angle surface and the cavity's surface under time-harmonic anti-plane shearing.Some calculating cases were plotted as examples to show the frequencies of incident waves,the medium's parameters,and the structure's geometry influence on the DSCF and EFICF.The calculation results indicate that the maximum number of DSCFs possible in presently used methods is nearly two or three times those on a semi-infinite piezoelectric medium,and the EFICF was more significant at a lower frequency.Dynamic analysis is of importance to a quarter-infinite piezoelectric medium with subsurface defects.
引文
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[9]SONG Tianshu,LI Dong,WANG Xinwang,et al.Dynamicanti-plane behaviors of a semi-infinite piezoelectric mediumwith a circular cavity and a crack near the surface[J].KeyEngineering Materials,2008,385-387:389-392.
[10]ACHENBACHJ.Wave propagation in elastic solids[M].Amsterdam:North-Holland Publishing Company,1973,108-116.
[11]史文谱,刘殿魁,宋永涛,等.直角平面内圆孔对稳态SH波的散射[J].应用数学和力学,2006,27(12):1417-1423.SHI Wenpu,LIUDiankui,SONG Yongtao,et al.Scatter-ing of circular cavity in right-angular planar space to steadySH-wave[J].Applied Mathematics and Mechanics,2006,27(12):1417-1423.
[12]折勇,齐辉,杨在林.SH波对直角平面区域内圆形孔洞的散射与地震动[J].应用力学学报,2008,25(3):392-397.SHI Yong,QI Hui,YANG Zailin.Scattering of SH-waveby circular cavity in right-angle plane and seismic groundmotion[J].Journal of Applied Mechanics,2008,25(3):392-397.
[13]SONG Tianshu,WANG Shilong.Dynamic stress on a semi-infinite piezoelectric medium with a circular cavity near thesurface[C]//Proceedings of the ASME International DesignEngineering Technical Conferences and Computers and Infor-mation in Engineering Conference(DETC2007).Las Vegas,US,2008,1:1741-1746.
[2]MEGUID S A,WANG X D.Dynamic antiplane behavior ofinteracting cracks in a piezoelectric medium[J].Interna-tional Journal of Fracture,1998,91:391-403.
[3]WANG X D,MEGUID S A.Effect of electromechanical cou-pling on the dynamic interaction of cracks in piezoelectric ma-terials[J].Acta Mechanica Sinica,2000,143:1-15.
[4]周振功,王彪.压电材料中两平行对称可导通裂纹断裂性能分析[J].应用数学和力学,2002,23(12):1211-1219.ZHOU Zhengong,WANG Biao.The behavior of two parallelsymmetric permeable cracks in piezoelectric materials[J].Applied Mathematics and Mechanics,2002,23(12):1211-1219.
[5]周振功,王彪.压电材料中两个非对称平行裂纹的基本解[J].应用数学和力学,2007,28(4):379-390.ZHOU Zhengong,WANG Biao.Basic solution of two paral-lel non-symmetric permeable cracks in piezoelectric materi-als[J].Applied Mathematics and Mechanics,2007,28(4):379-390.
[6]LI Xianfang,WANG Baolin.Anti-plane shear crack normalto and terminating at the interface of two bonded piezoelec-tric ceramics[J].International Journal of Solids And Struc-tures,2007,44:3796-3810.
[7]CHEN Z T,YU S W.Transient response of a cracked pie-zoelectric strip under arbitrary electro-mechanical impact[J].Acta Mechanica Sinica,1998,14(3):248-256.
[8]周志东,赵社戌,匡震邦.任意点载荷下含椭圆孔压电介质中广义应力和位移分析[J].上海交通大学学报,2004,38(8):1403-1407.ZHOU Zhidong,ZHAO Shexu,KUANG Zhenbang.Analy-sis of general stress and displacement in piezoelectric ceram-ics with an elliptic hole[J].Journal of Shanghai Jiao TongUniversity,2004,38(8):1403-1407.
[9]SONG Tianshu,LI Dong,WANG Xinwang,et al.Dynamicanti-plane behaviors of a semi-infinite piezoelectric mediumwith a circular cavity and a crack near the surface[J].KeyEngineering Materials,2008,385-387:389-392.
[10]ACHENBACHJ.Wave propagation in elastic solids[M].Amsterdam:North-Holland Publishing Company,1973,108-116.
[11]史文谱,刘殿魁,宋永涛,等.直角平面内圆孔对稳态SH波的散射[J].应用数学和力学,2006,27(12):1417-1423.SHI Wenpu,LIUDiankui,SONG Yongtao,et al.Scatter-ing of circular cavity in right-angular planar space to steadySH-wave[J].Applied Mathematics and Mechanics,2006,27(12):1417-1423.
[12]折勇,齐辉,杨在林.SH波对直角平面区域内圆形孔洞的散射与地震动[J].应用力学学报,2008,25(3):392-397.SHI Yong,QI Hui,YANG Zailin.Scattering of SH-waveby circular cavity in right-angle plane and seismic groundmotion[J].Journal of Applied Mechanics,2008,25(3):392-397.
[13]SONG Tianshu,WANG Shilong.Dynamic stress on a semi-infinite piezoelectric medium with a circular cavity near thesurface[C]//Proceedings of the ASME International DesignEngineering Technical Conferences and Computers and Infor-mation in Engineering Conference(DETC2007).Las Vegas,US,2008,1:1741-1746.
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