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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[1] PAO Y H, MOW C C, Achenbach J D. Diffraction of elastic waves and dynamic stress concentrations[J]. Journal of Applied Mechanics, 1973, 40(4):213-219. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=JJ0220516407 [2] COUSSY O. Scattering of SH-waves by a cylindrical inclusion presenting an interface crack[J]. CR Acad Sci Paris, 1982, 295:1043-1046. https://www.researchgate.net/publication/309224500_Scattering_of_SH_Wave_by_a_Cylindrical_Inclusion_and_a_Semi-Cylindrical_Hollow_Near_Vertical_Interface_Crack_in_the_Bi-Material_Half_Space [3] COUSSY O. Scattering of elastic waves by an inclusion with an interface crack[J]. Wave Motion, 1983, 6(3):223-236. doi: 10.1016-0165-2125(84)90026-X/ [4] 汪越胜, 王铎.SH波对有部分脱胶衬砌的圆形孔洞的散射[J].力学学报, 1994, 26(4):462-469. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK199400323665WANG Yuesheng, WANG Duo. Diffraction of SH-waves by a circular cavity with a particular debonded liner[J]. Acta Mechanica Sinica, 1994, 26(4):462-469. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK199400323665 [5] 汪越胜, 王铎.剪切波作用下圆弧形界面裂纹的动强度因子[J].固体力学学报, 1993, 14(4):362-367. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK000000699056WANG Yuesheng, WANG Duo. Dynamic stress intensity factors of circular arcshaped interface cracks subjected to shear waves[J]. Acta Solida Mechanics Sinica, 1993, 14(4):362-367. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=QK000000699056 [6] LEE V W, KARL J. Diffraction of SV waves by underground, circular, cylindrical cavities[J]. Soil Dynamics and Earthquake Engineering, 1992, 11(8):445-456. doi: 10.1016/0267-7261(92)90008-2 [7] QI Hui, YANG Jie, SHI Yong. Scattering of SH-wave by cylindrical inclusion near interface in bimaterial half-space[J]. Journal of Mechanics, 2011, 27(1):37-45. doi: 10.1017/jmech.2011.5 [8] 齐辉, 丁晓浩, 赵元博.双相介质弹性半空间垂直界面附近椭圆形夹杂对SH波的散射[J].振动与冲击, 2015, 34(24):76-81. http://d.old.wanfangdata.com.cn/Periodical/zdycj201524013QI Hui, DING Xiaohao, ZHAO Yuanbo. Scattering of SH-wave by an elliptic inclusion near vertical interface in a bi-material half-space[J]. Journal of Vibration and Shock, 2015, 34(24):76-81. http://d.old.wanfangdata.com.cn/Periodical/zdycj201524013 [9] 杨杰.半空间垂直界面裂纹及圆夹杂对SH波的散射[D].哈尔滨: 哈尔滨工程大学, 2012: 22-34. http://cdmd.cnki.com.cn/Article/CDMD-10217-1012518460.htm [10] LOEBER J F, SIH G C. Diffraction of antiplane shear waves by a finite ccrack[J]. Journal of the Acoustical Society of America, 1967, 44(1):90-98. doi: 10.1121/1.1911091 [11] 陈冬妮, 齐辉.SH波入射覆盖层半空间圆孔及圆夹杂的动力分析[J].哈尔滨工程大学学报, 2014, 35(2):171-176. http://d.old.wanfangdata.com.cn/Periodical/hebgcdxxb201402006CHEN Dongni, QI Hui. Dynamic analysis for circular cavity and inclusion impacted by SH-wave in a layered half-space[J]. Journal of Harbin Engineering University, 2014, 35(2):171-176. http://d.old.wanfangdata.com.cn/Periodical/hebgcdxxb201402006 [12] 张希萌, 齐辉, 项梦.半空间双相压电介质垂直边界附近圆孔对SH波的散射[J].爆炸与冲击, 2017, 37(4):591-599. http://www.bzycj.cn/CN/abstract/abstract9758.shtmlZHANG Ximeng, QI Hui, XIANG Meng. Scattering of SH-wave by a circular cavity near the vertical boundary[J]. Explosion and Shock Waves, 2017, 37(4):591-599. http://www.bzycj.cn/CN/abstract/abstract9758.shtml [13] 杨在林, 许华南, 黑宝平.半空间椭圆夹杂与裂纹对SH波的散射[J].振动与冲击, 2013, 32(11):56-61. doi: 10.3969/j.issn.1000-3835.2013.11.012YANG Zailin, XU Huanan, HEI Baoping. Interaction of elliptical and crack under incident SH-wave in a half-space[J]. Journal of Vibration and Shock, 2013, 32(11):56-61. doi: 10.3969/j.issn.1000-3835.2013.11.012 [14] 赵嘉喜, 齐辉, 杨在林.含有部分脱胶的浅埋圆夹杂对SH波的散射[J].岩土力学, 2009, 30(5):1297-1302. doi: 10.3969/j.issn.1000-7598.2009.05.018ZHAO Jiaxi, QI Hui, YANG Zailin. Scattering of SH-waves by a shallow buried cylindrical inclusion with a partially debonded curve in half space[J]. Rock and Soil Mechanics, 2009, 30(5):1297-1302. doi: 10.3969/j.issn.1000-7598.2009.05.018 [15] 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 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 [16] 赵元博, 齐辉, 丁晓浩, 等.SH波作用下地表软覆盖层中圆形夹杂的动应力分析[J].爆炸与冲击, 2017, 37(6):982-989. http://www.bzycj.cn/CN/abstract/abstract9823.shtmlZHAO Yuanbo, QI Hui, DING Xiaohao, et al. Dynamic analysis for shallow buried circular inclusion impacted by SH-wave in a softlayered half-space[J]. Explosion and Shock Waves, 2017, 37(6):982-989. http://www.bzycj.cn/CN/abstract/abstract9823.shtml [17] 陈志刚.平面SH波在浅埋椭圆柱形孔洞上的散射与应力集中[J].暨南大学学报, 2005, 26(3):324-330. doi: 10.3969/j.issn.1000-9965.2005.03.009CHEN Zhigang. Scattering of SH-wave by a shallow buried elliptic cylindrical cavity and dynamic stress concentration[J]. Journal of Jinan University, 2005, 26(3):324-330. doi: 10.3969/j.issn.1000-9965.2005.03.009 -
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