含孔半圆形凸起地形及多个孔洞对SH波的散射
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摘要
应用"契合"、复变函数及多极坐标法研究在平面SH波的作用之下,含有圆形孔洞的半圆形凸起地形与其附近的多个圆形孔洞的散射问题,研究了SH波对其动应力集中及地震动的影响.对问题求解时,将所研究的区域一分为二,成2个区域,并分别构造其波函数.最后在2个区域的公共边界上实施"契合",而得到问题的解答.最后给出了算例,分析讨论了地表位移幅值及圆形孔洞周边上的动应力集中系数的变化规律.结果表明,浅埋多圆孔的间距越小,对地表位移幅值和动应力集中系数的影响越大,当浅埋圆孔间距与凸起半径的比值达到400时,对地表位移的影响基本消失.
The antiplanar SH-deformation of a semi-cylindrical hill with a hole and several concentric circular cavities around it,and the influence of SH-waves on dynamic stress concentrations and ground motion were studied by using a "conjunction",complex functions,and the multi-polar-coordinate method.During the solving process,the domain was divided into two regions,and the scattering wave functions were constructed separately in each one.Then a conjunction was made at the common boundaries to find the solution to the problem.Computational examples are presented.Variation rules are discussed for the amplitudes of surface displacements and the dynamic stress concentration factors around the edges of circular cavities.It was concluded that the smaller the distances between the cavities,the greater the influences of displacement amplitude and the dynamic stress concentration factor(DSCF).When the ratio of the distances between cavities to the radius of the hill is more than 400,their inter-influence on displacements and DSCF basically dies away.
The antiplanar SH-deformation of a semi-cylindrical hill with a hole and several concentric circular cavities around it,and the influence of SH-waves on dynamic stress concentrations and ground motion were studied by using a "conjunction",complex functions,and the multi-polar-coordinate method.During the solving process,the domain was divided into two regions,and the scattering wave functions were constructed separately in each one.Then a conjunction was made at the common boundaries to find the solution to the problem.Computational examples are presented.Variation rules are discussed for the amplitudes of surface displacements and the dynamic stress concentration factors around the edges of circular cavities.It was concluded that the smaller the distances between the cavities,the greater the influences of displacement amplitude and the dynamic stress concentration factor(DSCF).When the ratio of the distances between cavities to the radius of the hill is more than 400,their inter-influence on displacements and DSCF basically dies away.
引文
[1]TRIFUNAC M D.Scattering of plane SH-waves by asemi-cylindrical canyon[J].Earthquake Engineering andStructural Dynamics,1973(1):267-281.
[2]LIU D K,HAN F.Scattering of plane SH-waves by cy-lindrical canyon of arbitrary shapes in anisotropic media[J].Acta Mechanica Sinica,1990,6(3):256-266.
[3]LIU D K,HAN F.Scattering of plane SH-wave by cy-lindrical canyon of arbitrary shapes[J].Int H Soil Dynand Ear Eng,1991,10(5):249-255.
[4]LEE V W,CHEN S,HUS I R.Antiplane diffractionfrom canyon above subsurface unlined tunner[J].ASCEEng Mech Div,1999,29(5):178-184.
[5]YUAN Xiaoming,HEN Fulu.Scattering of plane SH-waves by a semi-cylindrical hill[J].Earthquake Engi-neering and Structural Dynamics,1992(21):1091-1089.
[6]YUAN X M,LIAO Z P.Surface motion of a cylindricalhill of circular are cross-section for incident plane SH-waves[J].Soil Dyn and Ear Eng,1996,15:189-199.
[7]刘殿魁,许贻燕.各向异性介质中SH波与多个半圆形凹陷地形的相互作用[J].力学学报,1993,25(1):93-102.LIU Diankui,XU Yiyan.The interaction between SH-waves and multiple semi-cylindrical canyons in anisotrop-ic medium[J].Acta Mechanica Sinica,1993,25(1):93-102.
[8]崔志刚,曹新荣,刘殿魁.SH波对半圆形凸起地形的散射[J].地震工程与工程振动,1998,18(1):140-146.CUI Zhigang,CAO Xinrong,LIU Diankui.Scattering ofplane SH-waves by a semi-cylindrical hill[J].EarthquakeEngi and Engi Vibration,1998,18(1):140-146.
[9]李敏,刘殿魁.SH波入射时含圆形孔洞的半圆形凸起地形与其附近的圆形孔洞的相互作用[J].哈尔滨工程大学学报,2005,26(5):608-613.LI Min,LIU Diankui.Scattering of SH-wave by a semi-cylindrical hill with a hole above a subsurface cavity inhalf-space[J].Jourunal of Harbin Engineering Universi-ty,2005,26(5):608-613.
[10]刘殿魁,曹新荣,崔志刚.多个半圆形凸起地形对平面SH波散射[J].固体力学学报,1998(特刊):178-185.LIU Diankui,CAO Xinrong,CUI Zhigang.Scatteringof plane SH-waves by a semi-cylindrical hill[J].ActaMechanics Solid Sinica,1998(S.Issue):178-185.
[11]WANG G Q,LIU D K.Scattering of SH-wave by mul-tiple circular cavities in half space[J].Earthquake engi-neering and Engineering vibration,2002,1(1):36-44.
[12]刘殿魁,林宏.浅埋的圆形孔洞对SH波散射与地震动[J].爆炸与冲击,2003,23(1):6-12.LIU Diankui,LIN Hong.Antiplane of SH-waves abovea subsurface cavity[J].Explosion and Shock Waves,2003,23(1):6-12.
[13]刘殿魁,王宁伟.相邻多圆孔各向异性介质中SH波的散射[J].地震工程与工程振,1989,9(4):15-28.LIU Diankui,WANG Ningwei.Scattering of SH-waveby multiple circular cavities in anisotropic medium[J].Earthquake Engi and Engi Vibration,1989,9(4):15-28.
[14]刘殿魁,刘宏伟.P波对具有不等深凹陷地形的散射[J].固体力学学报,1997,18(4):295-300.LIU Diankui,LIU Hongwei.Scattering of P-waves bycanyons with variable depth-to-width ratio[J].ActaMechancs Solid Sinica,1997,18(4):295-300.
[15]黎在良,刘殿魁.固体中的波[M].北京:科学出版社,1995.
[16]LIU D K,GAI B Z,TAO G Y.Applications of themethod of complex functions to dynamic stress concen-trations[J].Wave Motion,1982,4:293-304.
[2]LIU D K,HAN F.Scattering of plane SH-waves by cy-lindrical canyon of arbitrary shapes in anisotropic media[J].Acta Mechanica Sinica,1990,6(3):256-266.
[3]LIU D K,HAN F.Scattering of plane SH-wave by cy-lindrical canyon of arbitrary shapes[J].Int H Soil Dynand Ear Eng,1991,10(5):249-255.
[4]LEE V W,CHEN S,HUS I R.Antiplane diffractionfrom canyon above subsurface unlined tunner[J].ASCEEng Mech Div,1999,29(5):178-184.
[5]YUAN Xiaoming,HEN Fulu.Scattering of plane SH-waves by a semi-cylindrical hill[J].Earthquake Engi-neering and Structural Dynamics,1992(21):1091-1089.
[6]YUAN X M,LIAO Z P.Surface motion of a cylindricalhill of circular are cross-section for incident plane SH-waves[J].Soil Dyn and Ear Eng,1996,15:189-199.
[7]刘殿魁,许贻燕.各向异性介质中SH波与多个半圆形凹陷地形的相互作用[J].力学学报,1993,25(1):93-102.LIU Diankui,XU Yiyan.The interaction between SH-waves and multiple semi-cylindrical canyons in anisotrop-ic medium[J].Acta Mechanica Sinica,1993,25(1):93-102.
[8]崔志刚,曹新荣,刘殿魁.SH波对半圆形凸起地形的散射[J].地震工程与工程振动,1998,18(1):140-146.CUI Zhigang,CAO Xinrong,LIU Diankui.Scattering ofplane SH-waves by a semi-cylindrical hill[J].EarthquakeEngi and Engi Vibration,1998,18(1):140-146.
[9]李敏,刘殿魁.SH波入射时含圆形孔洞的半圆形凸起地形与其附近的圆形孔洞的相互作用[J].哈尔滨工程大学学报,2005,26(5):608-613.LI Min,LIU Diankui.Scattering of SH-wave by a semi-cylindrical hill with a hole above a subsurface cavity inhalf-space[J].Jourunal of Harbin Engineering Universi-ty,2005,26(5):608-613.
[10]刘殿魁,曹新荣,崔志刚.多个半圆形凸起地形对平面SH波散射[J].固体力学学报,1998(特刊):178-185.LIU Diankui,CAO Xinrong,CUI Zhigang.Scatteringof plane SH-waves by a semi-cylindrical hill[J].ActaMechanics Solid Sinica,1998(S.Issue):178-185.
[11]WANG G Q,LIU D K.Scattering of SH-wave by mul-tiple circular cavities in half space[J].Earthquake engi-neering and Engineering vibration,2002,1(1):36-44.
[12]刘殿魁,林宏.浅埋的圆形孔洞对SH波散射与地震动[J].爆炸与冲击,2003,23(1):6-12.LIU Diankui,LIN Hong.Antiplane of SH-waves abovea subsurface cavity[J].Explosion and Shock Waves,2003,23(1):6-12.
[13]刘殿魁,王宁伟.相邻多圆孔各向异性介质中SH波的散射[J].地震工程与工程振,1989,9(4):15-28.LIU Diankui,WANG Ningwei.Scattering of SH-waveby multiple circular cavities in anisotropic medium[J].Earthquake Engi and Engi Vibration,1989,9(4):15-28.
[14]刘殿魁,刘宏伟.P波对具有不等深凹陷地形的散射[J].固体力学学报,1997,18(4):295-300.LIU Diankui,LIU Hongwei.Scattering of P-waves bycanyons with variable depth-to-width ratio[J].ActaMechancs Solid Sinica,1997,18(4):295-300.
[15]黎在良,刘殿魁.固体中的波[M].北京:科学出版社,1995.
[16]LIU D K,GAI B Z,TAO G Y.Applications of themethod of complex functions to dynamic stress concen-trations[J].Wave Motion,1982,4:293-304.
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