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
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摘要
采用Green函数及复变函数方法研究了SH波入射到双相介质半空间时,浅埋任意位置圆形夹杂的动力响应问题。首先,利用"镜像"法构造满足直角平面自由边界条件的散射波场解答,进而求出该文所需的Green函数;其次,利用"契合"思想,将模型沿着垂直界面剖分为两个直角域,并利用界面连续性条件及Green函数建立待解外力系的第一类Fredholm积分方程组;最后,通过具体算例给出了圆形弹性夹杂周边的动应力集中系数。结果显示:界面、自由边界、圆形夹杂、入射波数等因素均对动应力集中系数有影响。
Green's function and complex function methods are used here to investigate the problem of the dynamic response for shallowly buried circular inclusions of arbitrary positions impacted by SH-wave in a bi-material half space.Firstly,the expression of the scattering wave field was constructed,satisfying the free boundary conditions in a right-angle plane by the method of 'image',then Green's function was constructed.Secondly,the bi-material media was divided into two parts along the vertical interface using the idea of interface 'conjunction',then a series of Fredholm integral equations of first kind for determining the unknown forces could be set up through continuity conditions on the surface and Green's function.Finally,some examples for the dynamic stress concentration factor of the cylindrical elastic inclusion are given.Numerical results show that the dynamic stress concentration factor is influenced by the interface,free boundary,circular inclusion,incident wave and so on.
Green's function and complex function methods are used here to investigate the problem of the dynamic response for shallowly buried circular inclusions of arbitrary positions impacted by SH-wave in a bi-material half space.Firstly,the expression of the scattering wave field was constructed,satisfying the free boundary conditions in a right-angle plane by the method of 'image',then Green's function was constructed.Secondly,the bi-material media was divided into two parts along the vertical interface using the idea of interface 'conjunction',then a series of Fredholm integral equations of first kind for determining the unknown forces could be set up through continuity conditions on the surface and Green's function.Finally,some examples for the dynamic stress concentration factor of the cylindrical elastic inclusion are given.Numerical results show that the dynamic stress concentration factor is influenced by the interface,free boundary,circular inclusion,incident wave and so on.
引文
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[11]刘殿魁,杨在林,刘建百.界面可移动圆柱形刚性夹杂对SH波散射及动应力集中[J].哈尔滨建筑大学学报,2001,34(6):1―7.Liu Diankui,Yang Zailin,Liu Jianbai.Scattering anddynamic stress concentration of SH-wave by removablerigid cylindrical interface inclusion[J].Journal of HarbinUniversity of Civil Engineering&Architecture,2001,34(6):1―7.(in Chinese)
[12]刘殿魁,史守峡.界面上圆形衬砌结构对平面SH波散射[J].力学学报,2002,34(5):796―803.Liu Diankui,Shi Shouxia.The Scattering of planeSH-wave by circular interface cavity with lining[J].ActaMechanica Sinica,2002,34(5):796―803.(in Chinese)
[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―204.Liu Diankui,Lin Hong.Scattering of SH-waves bycircular cavities near bimaterial interface[J].ActaMechanica Solida Sinica,2003,24(2):197―204.(inChinese)
[14]Shi Wenpu,Liu Diankui,Song Yongtao.Scattering ofcircular cavity in right-angle plane space to steadySH-wave[J].Applied Mathematics and Mechanics,2006,27(12):1619―1626.
[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.Lin Hong,Liu Diankui.Scattering of SH-wave around acircular cavity in half space[J].Earthquake Engineeringand Engineering Vibration,2002,22(2):9―16.(inChinese)
[2]Chen J T,Chen P Y,Chen C T.Surface motion ofmultiple alluvial valleys for incident plane SH-waves byusing a semi-analytical approach[J].Soil Dynamics andEarthquake Engineering,2008,28:58―72.
[3]齐辉,王艳,刘殿魁.半无限空间界面附近SH波对圆形衬砌的散射[J].地震工程与工程振动,2003,23(3):41―46.Qi Hui,Wang Yan,Liu Diankui.Dynamic analysis ofshallow-embedded lining structure by incident SH-wave[J].Earthquake Engineering and Engineering Vibration,2003,23(3):41―46.(in Chinese)
[4]陈志刚,刘殿魁.SH波冲击下浅埋任意形孔洞的动力分析[J].地震工程与工程振动,2004,24(4):32―36.Chen Zhigang,Liu Diankui.Dynamic response on ashallowly buried cavity of arbitrary shape impacted byvertical SH-wave[J].Earthquake Engineering andEngineering Vibration,2004,24(4):32―36.(in Chinese)
[5]刘刚,李宏亮,刘殿魁.SH波对浅埋裂纹的半圆形凹陷地形的散射[J].爆炸与冲击,2007,27(2):171―178.Liu Gang,Li Hongliang,Liu Diankui.Scattering of asemi-cylindrical canyon and a crack with incident SHwaves[J].Explosion and Shock Waves,2007,27(2):171―178.(in Chinese)
[6]Liang Jianwen,Luo Hao,Vincent W Lee.Diffraction ofplane SH waves by a semi-circular cavity in half-space[J].Earthquake Science,2010,23:5―12.
[7]齐辉,折勇,李宏亮.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.Qi Hui,Shi Yong,Li Hongliang.Dynamic analysis forscattering of SH-wave by circular cavities near bimaterialinterfaces in a vertical half-space[J].Explosion andShock Waves,2009,29(1):73―79.(in Chinese)
[8]南景福,齐辉,折勇.垂直半空间界面裂纹及附近圆孔对SH波的散射[J].工程力学,2009,26(5):245―250,256.Nan Jingfu,Qi Hui,She Yong.Scattering of SH-wave byinterface crack and neighboring circular cavity inbi-material vertical half-space[J].EngineeringMechanics,2009,26(5):245―250,256.(in Chinese)
[9]刘殿魁,刘宏伟.SH波散射与界面圆孔的动应力集中[J].力学学报,1998,30(5):597―604.Liu Diankui,Liu Hongwei.Scattering and dynamic stressconcentration of SH-wave by interface circular hole[J].Acta Mechanica Sinica,1998,30(5):597―604.(inChinese)
[10]史守峡,刘殿魁.SH波与界面多圆孔的散射及动应力集中[J].力学学报,2001,33(1):60―70.Shi Shouxia,Liu Diankui.Dynamic stress concentration&scattering of SH-wave by interface multiple circlecanyons[J].Acta Mechanica Sinica,2001,33(1):60―70.(in Chinese)
[11]刘殿魁,杨在林,刘建百.界面可移动圆柱形刚性夹杂对SH波散射及动应力集中[J].哈尔滨建筑大学学报,2001,34(6):1―7.Liu Diankui,Yang Zailin,Liu Jianbai.Scattering anddynamic stress concentration of SH-wave by removablerigid cylindrical interface inclusion[J].Journal of HarbinUniversity of Civil Engineering&Architecture,2001,34(6):1―7.(in Chinese)
[12]刘殿魁,史守峡.界面上圆形衬砌结构对平面SH波散射[J].力学学报,2002,34(5):796―803.Liu Diankui,Shi Shouxia.The Scattering of planeSH-wave by circular interface cavity with lining[J].ActaMechanica Sinica,2002,34(5):796―803.(in Chinese)
[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―204.Liu Diankui,Lin Hong.Scattering of SH-waves bycircular cavities near bimaterial interface[J].ActaMechanica Solida Sinica,2003,24(2):197―204.(inChinese)
[14]Shi Wenpu,Liu Diankui,Song Yongtao.Scattering ofcircular cavity in right-angle plane space to steadySH-wave[J].Applied Mathematics and Mechanics,2006,27(12):1619―1626.
[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.Lin Hong,Liu Diankui.Scattering of SH-wave around acircular cavity in half space[J].Earthquake Engineeringand Engineering Vibration,2002,22(2):9―16.(inChinese)
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