双相介质半空间中圆孔对透射SH波的稳态分析

齐辉; 蔡立明; 罗广龙; 潘向南; 杨杰; 王宪章; 李国文; 蒋敬江

doi:10.11883/1001-1455(2015)04-0591-08

双相介质半空间中圆孔对透射SH波的稳态分析

doi: 10.11883/1001-1455(2015)04-0591-08

1.
哈尔滨工程大学航天与建筑工程学院，黑龙江哈尔滨 150001
2.
上海电机学院机械学院，上海 201306
3.
中建一局总承包公司，北京 100070

基金项目: 国家自然科学基金项目(51379048)

详细信息

作者简介:
齐辉(1963-), 男, 博士, 教授

通讯作者:
潘向南, panxiangnan@hrbeu.edu.cn

中图分类号: O343
计量
- 文章访问数: 3007
- HTML全文浏览量: 295
- PDF下载量: 480
- 被引次数: 0
出版历程
- 收稿日期: 2013-12-04
- 修回日期: 2014-03-01
- 刊出日期: 2015-07-25

Steady state analysis for circular cavity impacted by transmitted SH wave in a bi-material half space

1.
College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang, China
2.
School of Mechanical Engineering, Shanghai Dianji University, Shanghai 201306, China
3.
China Construction First Engineering Division Corp. Ltd., Beijing 100070, China

摘要

摘要: 研究了平面SH波在半空间双相弹性介质中的传播。通过Green函数和积分方程方法，按照复变函数描述，对透射波被圆孔散射的情况进行稳态分析。将双相介质半空间沿界面剖分为1/4空间介质Ⅰ和含圆孔的1/4空间介质Ⅱ，分别构造了介质Ⅰ和介质Ⅱ中反平面点源荷载的Green函数，按双相介质中平面SH波的处理方法，给出介质Ⅰ和介质Ⅱ中的平面位移波，两种介质之间的相互作用力与对应Green函数的乘积沿界面的积分与平面位移波叠加得到介质Ⅰ和介质Ⅱ中的全部位移场。按照界面的位移连续条件，定解积分方程组，得到问题的稳态解，并给出圆孔位置和介质参数对散射的影响。
- 固体力学 /
- 散射 /
- Green函数 /
- SH波 /
- 圆孔 /
- 双相介质半空间 /
- 振动与波
Abstract: To study the way that the plane SH wave propagating in an elastic bi-material half space from medium Ⅰ to medium Ⅱ, the steady-state scattering of the transmitted wave by a circular cavity is analyzed by using Green function and integral equation methods on complex function description. The bi-material half space is divided into a quarter space medium Ⅰ and a quarter space medium Ⅱ with a circular cavity in it. Their Green functions are constructed as anti-plane point source response problem respectively. The total displacement fields of medium Ⅰ and medium Ⅱ are formulated as two parts' vector sum. The first part is interfacial integral of interactive force multiplied by corresponding Green function. The second part is plane displacement field formed by omitting the circular cavity. Steady state solution is obtained by determining the integral equations along interface with displacement continuity. Numerical results are presented to reveal the effects of locations and material parameters on circular cavity scattering.
- solid mechanics /
- scattering /
- Green function /
- SH wave /
- a circular cavity /
- a bi-material half space /
- vibration and wave

HTML全文

图 1 半空间双相介质中的圆孔

Figure 1. Circular cavity in a bi-material half space

下载: 全尺寸图片幻灯片

图 2 等价问题

Figure 2. Equivalent issue

下载: 全尺寸图片幻灯片

图 3 介质Ⅱ中的Green函数

Figure 3. Green function in medium Ⅱ

下载: 全尺寸图片幻灯片

图 4 位移波场的契合

Figure 4. Conjunction of displacement wave field

下载: 全尺寸图片幻灯片

图 5 动应力集中因子在圆孔边沿的分布

Figure 5. Distribution of dynamic stress concentrations factors around the cylindrical cavity

下载: 全尺寸图片幻灯片

图 6 标准化位移幅值在水平边界上的分布

Figure 6. Distribution of normalized displacement amplitude along the horizontal bound

下载: 全尺寸图片幻灯片

参考文献(18)

[1]	Achenbach J D. Wave propagation in elastic solids[M]. Netherlands, Amsterdam: North-Holland, 1973.
[2]	胡德绥.弹性波动力学[M].北京: 地质出版社, 1989.
[3]	Ying C F, Truell R. Scattering of plane longitudinal wave by a spherical obstacle in an isotropically elastic solid[J]. Journal of Applied Physics, 1956, 27(9): 1086-1097. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5121709
[4]	PaoY H, Mow C C. Diffraction of elastic waves and dynamic wtress concentrations[M]. New York: Crane & Russak, 1973.
[5]	Liu D K, Gai B Z, Tao G Y. Applications of the method of complex functions to dynamic stress concentrations[J]. Wave Motion, 1982, 4(3): 293-304. http://www.sciencedirect.com/science/article/pii/0165212582900257
[6]	刘殿魁.各向异性介质中Ⅲ型裂缝的动力分析[J].地震工程与工程振动, 1991, 11(2): 29-38. http://www.cqvip.com/QK/95364X/19912/462508.html Liu Dian-kui. Analysis of dynamic stresses of mode Ⅲ crack in anisotropic materials[J]. Earthquake Engineering and Engineering Vibration, 1991, 11(2): 29-38. http://www.cqvip.com/QK/95364X/19912/462508.html
[7]	刘殿魁, 刘宏伟. SH波散射与界面圆孔附近的动应力集中[J].力学学报, 1998, 30(5): 597-604. Liu Dian-kui, Liu Hong-wei. Scattering and dynamic stress concentration of SH-wave by interface circular hole[J]. Acta Mechanica Sinica, 1998, 30(5): 598-604.
[8]	刘殿魁, 田家勇. SH波对界面圆柱形弹性夹杂散射及动应力集中[J].爆炸与冲击, 1999, 19(2): 115-122. http://www.bzycj.cn/article/id/10328 Liu Dian-kui, Tian Jia-yong. Scattering and dynamic stress concentration of SH-wave by interface cylindrical elastic inclusion[J]. Explosion and Shock Waves, 1999, 19(2): 115-122. http://www.bzycj.cn/article/id/10328
[9]	史文谱, 刘殿魁, 宋永涛.直角平面区域内固定圆形刚性夹杂问题的Green函数解[J].固体力学学报, 2006, 27(2): 207-212. http://www.cqvip.com/Main/Detail.aspx?id=22435451 Shi Wen-pu, Liu Dian-kui, Song Yong-tao. The anti-plane Green function solution of the problem of a fixed rigid circular inclusion in right-angle plane[J]. Acta Mechanica Solida Sinica, 2006, 27(2): 207-212. http://www.cqvip.com/Main/Detail.aspx?id=22435451
[10]	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): 1619-1626. http://d.wanfangdata.com.cn/Periodical_yysxhlx200612004.aspx Shi Wen-pu, Liu Dian-kui, Song Yong-tao, et al. Scattering of circular cavity in right-angle plane space to steady SH-wave[J]. Applied Mathematics and Mechanics, 2006, 27(12): 1619-1626. http://d.wanfangdata.com.cn/Periodical_yysxhlx200612004.aspx
[11]	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. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=yylxxb200803009 Shi Yong, Qi Hui, Yang Zai-lin. Scattering of SH-wave by circular cavity in right-angle plane and seismic ground motion[J]. Chinese Journal of Applied Mechanics, 2008, 25(3): 392-397. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=yylxxb200803009
[12]	张根昌, 齐辉, 刘平安. SH波对直角平面区域内圆形衬砌的散射与地震动[J].力学与实践, 2013, 35(1): 60-66. http://d.wanfangdata.com.cn/Periodical/yylxxb200803009 Zhang Gen-chang, Qi Hui, Liu Ping-an. Scattering of SH-wave by circular lining in right-angle plane and seismic ground motion[J]. Mechanics in Engineering, 2013, 35(1): 60-66. http://d.wanfangdata.com.cn/Periodical/yylxxb200803009
[13]	刘殿魁, 林宏. SH波对双相介质界面附近圆形孔洞的散射[J].固体力学学报, 2003, 24(2): 197-2004. http://d.wanfangdata.com.cn/Periodical/gtlxxb200302010 Liu Dian-kui, Lin Hong. Scattering of SH-waves by circular cavities near bi-material interface[J]. Acta Mechanica Solida Sinica, 2003, 24(2): 197-2004. http://d.wanfangdata.com.cn/Periodical/gtlxxb200302010
[14]	齐辉, 折勇, 李宏亮, 等. SH波入射时垂直半空间中双相介质界面附近圆孔的动力分析[J].爆炸与冲击, 2009, 29(1): 73-79. doi: 10.11883/1001-1455(2009)01-0073-07 Qi Hui, Shi Yong, Li Hong-liang, et al. Dynamic analysis for scattering of SH-wave by circular cavities near bimaterial interfaces in a vertical half-space[J]. Explosion and Shock Waves, 2009, 29(1): 73-79. doi: 10.11883/1001-1455(2009)01-0073-07
[15]	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.cnki.com.cn/Article/CJFDTotal-GCLX201207048.htm Qi 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.cnki.com.cn/Article/CJFDTotal-GCLX201207048.htm
[16]	Qi H, Yang J, Shi Y. Scattering of SH-wave by cylindrical inclusion near interface in bi-material half space[J]. Journal of Mechanics, 2011, 27(1): 37-45. http://journals.cambridge.org/abstract_S1727719111000050
[17]	Qi H, Yang J, Shi Y, Tian J Y. Dynamic analysis for circular inclusion near interfacial crack impacted by SH wave in half space[J]. Journal of Mechanics, 2012, 28(1): 143-151. http://www.sciencedirect.com/science/article/pii/S0997753812000319
[18]	Qi H, Yang J. Dynamic analysis for circular inclusions of arbitrary positions near interfacial crack impacted by SH-wave in half-space[J]. European Journal of Mechanics: A: Solids, 2012, 36: 18-24. http://www.sciencedirect.com/science/article/pii/S0997753812000319