双相介质半空间内椭圆夹杂对透射SH波的散射

齐辉; 龚曲; 曾庆友

doi:10.11883/bzycj-2016-0149

双相介质半空间内椭圆夹杂对透射SH波的散射

doi: 10.11883/bzycj-2016-0149

哈尔滨工程大学航天与建筑工程学院, 黑龙江哈尔滨 150001

基金项目:

黑龙江省自然科学基金项目 A201404

详细信息

作者简介:
齐辉(1963-), 男, 博士, 教授, 博导, qihui205@sina.com

中图分类号: O347.3;O343.1
计量
- 文章访问数: 5259
- HTML全文浏览量: 1981
- PDF下载量: 132
- 被引次数: 0
出版历程
- 收稿日期: 2016-05-13
- 修回日期: 2016-07-08
- 刊出日期: 2018-05-25

Scattering of transmission SH-wave by elliptic inclusion in bi-material half-pace

College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang, China

摘要

摘要: 为探究双相介质弹性半空间内椭圆弹性夹杂对透射SH波的散射问题，主要采用Green函数法、复变函数法、保角映射法和极坐标移动技术。首先，引入复变量并在复平面上运用保角映射的方法将椭圆边界映射为单位圆边界；然后，将双相介质沿垂直边界剖开分成两个四分之一空间，在剖分面上作用附加力系使SH波在垂直边界上满足位移和应力连续的条件，并构造四分之一空间内点源荷载作用下的Green函数位移场；进而，利用"契合"的思想在垂直边界上建立定解积分方程组，并利用SH波衰减的性质进行有限项截断来求解未知附加力系。最后，通过具体算例得出在不同参数情况下椭圆夹杂周边动应力集中因子分布情况。结果得知，SH波的入射角度和频率以及介质的性质对夹杂周边动应力集中分布有一定影响。
- 散射 /
- 透射SH波 /
- 双相介质 /
- 椭圆夹杂 /
- 动应力集中因子
Abstract: In this paper we studied the scattering of the transmission SH-wave form by elliptic elastic inclusions in a bi-material half-space using mainly the Green function, the complex function, the conformal mapping and the polar coordinate. Firstly, by introducing the complex variables and using the conformal mapping, we mapped the elliptic boundary into a unit circle. Next, by dividing the double-phase medium along the vertical boundaries into two quarter-spaces and adding a force system on the subdivision surface to make the SH wave satisfy the displacement and stress continuity conditions in the vertical boundary, we constructed a quarter-space Green function of displacement field. Then, we established an additional force system of integro differential equations in the vertical interface using the "conjunction" technique, and solved the unknown additional force system using the effective truncation. Finally, we presented and discussed the distribution of the dynamic stress concentration factor around the elliptic inclusion under the conditions of different parameters. The results show that the SH-wave incident angle and frequency, and the media both have influences on the distribution of the dynamic stress concentration factor.
- scattering /
- transmission SH-wave /
- bi-material /
- elliptic inclusion /
- dynamic stress concentration factor

HTML全文

图 1 理论模型

Figure 1. Theoretical model

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图 2 虚设点源模型

Figure 2. Model of dummy point source loads

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图 3 剖分面模型

Figure 3. Model of cutaway interface

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图 4 SH波以不同角度入射时动应力集中因子的分布情况

Figure 4. Distribution of dynamic stress concentration factor with different incident angles disturbed by SH wave

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图 5 SH波水平向入射时动应力集中因子随k₂₁的分布情况

Figure 5. Distribution of dynamic stress concentration factor around the elliptic inclusion edge with k₂₁ disturbed by SH wave horizontally

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图 6 SH波水平向入射时动应力集中因子随k₃₁的分布情况

Figure 6. Distribution of dynamic stress concentration factor around the elliptic inclusion edge with k₃₁ disturbed by SH wave horizontally

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图 7 SH波水平向入射时动应力集中因子随h/b的分布情况

Figure 7. Distribution of dynamic stress concentration factor around the elliptic inclusion edge with h/b disturbed by SH wave horizontally

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参考文献(8)

[1]	齐辉, 蔡立明, 罗广龙, 等.双相介质半空间中圆孔对透射SH波的稳态分析[J].爆炸与冲击, 2015, 35(4):591-598. doi: 10.11883/1001-1455(2015)04-0591-08 QI Hui, CAI Liming, LUO Guanglong. Steady state analysis for circular cavity impacted by transmitted SH wave in a bi-material half space[J]. Explosion and Shock Waves, 2015, 35(4):591-598. doi: 10.11883/1001-1455(2015)04-0591-08
[2]	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 Hongliang, et al.Dynamic analysis for scattering of SH-wave by circular cavities near bi-material 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
[3]	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):197-204. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=gtlxxb200302010 LIU Diankui, LIN Hong. Scattering of SH-waves by circular cavities near bimaterial interface[J]. Acta Mechanica Solida Sinica, 2003, 24(2):197-204. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=gtlxxb200302010
[4]	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://industry.wanfangdata.com.cn/dl/Detail/Periodical?id=Periodical_zdycj201524013 QI 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://industry.wanfangdata.com.cn/dl/Detail/Periodical?id=Periodical_zdycj201524013
[5]	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. doi: 10.6052/j.issn.1000-4750.2010.09.0680 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. doi: 10.6052/j.issn.1000-4750.2010.09.0680
[6]	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 YANG Jie. Scattering of SH-wave by vertical interface crack and circular inclusions in half space[D]. Harbin: Harbin Engineering University, 2012: 22-34. http://cdmd.cnki.com.cn/Article/CDMD-10217-1012518460.htm
[7]	杨在林, 许华南, 黑宝平.SH波上方垂直入射时界面附近椭圆夹杂与裂纹的动态响应[J].岩土力学, 2013, 34(8):2378-2384. http://www.cnki.com.cn/Article/CJFDTotal-YTLX201308054.htm YANG Zailin, XU Huanan, HEI Baoping. Dynamic response of elliptical inclusion and crack neat interface under vertically incident SH-wave from above[J]. Rock and Soil Mechanics, 2013, 34(8):2378-2384. http://www.cnki.com.cn/Article/CJFDTotal-YTLX201308054.htm
[8]	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.1000-3835.2013.11.012 YANG 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