浅埋圆形孔洞附近的弧形凸起对SH波的散射
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摘要
采用“契合”的思想,给出了地下孔洞与地面上的弧形凸起地形对SH波散射问题的解决方法.求解过程中将整个求解区域分割为2个部分处理,包括弧形凸起地形在内的一个圆形区域Ⅰ、区域Ⅱ.在区域Ⅰ中构造一个弧形部分边界应力为零,而其余部分位移、应力任意的驻波解,在区域Ⅱ中构造出弧形凹陷和浅埋圆孔的散射波,且要求其满足水平界面上应力为零的约束条件.通过坐标移动,满足“公共边界”的位移应力连续条件和地下孔洞的边界条件,建立起求解该问题的无穷代数方程组.给出了分析例题和数值结果,结果表明不同的弧形凸起对SH波的散射作用不同.
The scattering of SH-waves by an arc-shaped cylindrical hill above a subsurface cavity,or canyon,is studied based on the 'conjunction' concept,using complex functions and the multi-polar coordinate method.To solve the problem,the half-space is divided into two parts,creating one circular domain which included the boundary of the hill,with the rest as the second domain.A solution was constructed in the circular domain which satisfied the requirements that stress be zero at the hill edge and be arbitrary in the other part.The second domain contains the arc-shaped cylindrical canyon and subsurface cavity,in which scattered wave functions is constructed which satisfy the requirement of null stress on the horizontal surface.Then,by using the moving coordinate method,the two solutions are conjoined at the junction interface,which should satisfy the boundary condition at the subsurface cavity edge.The problem to be solved can then be reduced to a series of infinite linear algebraic equations.Examples of computational results of surface displacement are provided,indicating that various arc-shaped cylindrical hills will generate different scattering action for SH waves.
The scattering of SH-waves by an arc-shaped cylindrical hill above a subsurface cavity,or canyon,is studied based on the 'conjunction' concept,using complex functions and the multi-polar coordinate method.To solve the problem,the half-space is divided into two parts,creating one circular domain which included the boundary of the hill,with the rest as the second domain.A solution was constructed in the circular domain which satisfied the requirements that stress be zero at the hill edge and be arbitrary in the other part.The second domain contains the arc-shaped cylindrical canyon and subsurface cavity,in which scattered wave functions is constructed which satisfy the requirement of null stress on the horizontal surface.Then,by using the moving coordinate method,the two solutions are conjoined at the junction interface,which should satisfy the boundary condition at the subsurface cavity edge.The problem to be solved can then be reduced to a series of infinite linear algebraic equations.Examples of computational results of surface displacement are provided,indicating that various arc-shaped cylindrical hills will generate different scattering action for SH waves.
引文
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[4]YUAN Xiaoming,MEN Fulu.Scattering of plane SH-waves by a semi-cylindrical hill[J].Earthq Eng andStruct Dynamics,1992(21):1091-1098.
[5]崔志刚,曹欣荣,刘殿魁.SH波对弧形凸起地形的散射[J].地震工程与工程振动,1998,18(1):140-146.CUI Zhigang,CAO Xinrong,LIU Diankui.Scattering ofSH-wave around an arc-shaped cylindrical hill[J].Earth-quake Engineering and Engineering Vibration,1998,18(1):140-146.
[6]刘殿魁,曹欣荣,崔志刚.多个弧形凸起地形对平面SH波散射[J].固体力学学报,1998(特刊):178-185.LIU Diankui,CAO Xinrong,CUI Zhigang.AntiplaneSH-deformation of mult-arcshaped cylindrical hill[J].Acta Mechnica Solida Sinica,1998(special):178-185.
[7]LEE V W,MANOOGIAN M E.Surface motion abovean arbitrary shape undergrand cavity for incident SHwave[J].European Earthquake Engineering,1995,8(1):3-11.
[8]LEE V W,CHEN S,HSU I R.Antiplane diffractionfrom canyon above subsurface unlined tunner[J].EngMech Div,ASCE,1999,125(2):668-674.
[9]刘殿魁,许贻燕.各向异性介质中SH波与多个弧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 of plane SH-wave and non-circular cavity surfaced with lining in ani-sotropic media[J].Chinese Journal of Theoretical Ap-plied Mechanics,1993,25(1):93-102.
[10]林宏,史文谱,刘殿魁.SH波入射时浅埋结构的动力分析[J].哈尔滨工程大学学报,2001,22(3):120-123.LIN Hong,SHI Wenpu,LIU Diankui.Dynamic analy-sis for shallow-embedded lining structure impacted byincident SH-wave[J].Journal of Harbin EngineeringUniversity,2001,22(3):120-123.
[2]LIU Diankui,HAN Feng.Scattering of plane SH-wavesby cylindrical canyon of arbitrary shape in anisotropicmedia[J].Acta Mechanics Sinica,1990,6(3):256-260.
[3]LIU Diankui,HAN Feng.Scattering of plane SH-wavesby a cylindrical canyon of arbitrary shape[J].Dynamicand Earthquake Engineering,1991,10(5):249-255.
[4]YUAN Xiaoming,MEN Fulu.Scattering of plane SH-waves by a semi-cylindrical hill[J].Earthq Eng andStruct Dynamics,1992(21):1091-1098.
[5]崔志刚,曹欣荣,刘殿魁.SH波对弧形凸起地形的散射[J].地震工程与工程振动,1998,18(1):140-146.CUI Zhigang,CAO Xinrong,LIU Diankui.Scattering ofSH-wave around an arc-shaped cylindrical hill[J].Earth-quake Engineering and Engineering Vibration,1998,18(1):140-146.
[6]刘殿魁,曹欣荣,崔志刚.多个弧形凸起地形对平面SH波散射[J].固体力学学报,1998(特刊):178-185.LIU Diankui,CAO Xinrong,CUI Zhigang.AntiplaneSH-deformation of mult-arcshaped cylindrical hill[J].Acta Mechnica Solida Sinica,1998(special):178-185.
[7]LEE V W,MANOOGIAN M E.Surface motion abovean arbitrary shape undergrand cavity for incident SHwave[J].European Earthquake Engineering,1995,8(1):3-11.
[8]LEE V W,CHEN S,HSU I R.Antiplane diffractionfrom canyon above subsurface unlined tunner[J].EngMech Div,ASCE,1999,125(2):668-674.
[9]刘殿魁,许贻燕.各向异性介质中SH波与多个弧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 of plane SH-wave and non-circular cavity surfaced with lining in ani-sotropic media[J].Chinese Journal of Theoretical Ap-plied Mechanics,1993,25(1):93-102.
[10]林宏,史文谱,刘殿魁.SH波入射时浅埋结构的动力分析[J].哈尔滨工程大学学报,2001,22(3):120-123.LIN Hong,SHI Wenpu,LIU Diankui.Dynamic analy-sis for shallow-embedded lining structure impacted byincident SH-wave[J].Journal of Harbin EngineeringUniversity,2001,22(3):120-123.
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