含有部分脱胶的浅埋圆衬砌对SH波的散射
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摘要
采用复变函数法研究了含有部分脱胶的浅埋圆形衬砌对SH波的散射问题.首先,将所研究的区域分成两个域,在圆形衬砌中构造一个满足脱胶部分应力自由的散射波函数,将其展开为含有一个待定系数的Fourier级数;而在介质半空间中应满足脱胶部分应力自由,公共边界处位移和应力连续的边界条件.然后,在"公共边界"上实施"契合",与此同时,可构造出脱胶结构,进而得到求解该问题的无穷代数方程组.最后,针对目前工程上应用较广的两种典型浅埋衬砌进行算例分析,给出了地表位移的数值结果,并讨论了入射波参数、脱胶位置以及埋深对地表位移的影响结果.
The scattering of SH-waves by a shallow buried circular liner with a partially debonded region in a half space is studied by analytical function method.Firstly,the solution domain is divided into two parts.The scattering wave function in the circular liner is constructed with vanished stress on the debonded region.Then,the wave function is expanded into Fourier series.In the half space,the boundary condition of the medium should satisfy the vanished stress on the the debonded region and the continuous stress and displacement on the remainder boundary of the elastic inclusion.The "conjunction" is applied on the common boundary and the debonded region is constructed.A set of infinite algebraic equations to solve this problem are obtained.In the end,numerical examples of the surface displacement about two classical kinds of circular liner used widely in engineering are presented,the influences by the incident wave parameters,the position of debonded region and the depth of circular liners are discussed.
The scattering of SH-waves by a shallow buried circular liner with a partially debonded region in a half space is studied by analytical function method.Firstly,the solution domain is divided into two parts.The scattering wave function in the circular liner is constructed with vanished stress on the debonded region.Then,the wave function is expanded into Fourier series.In the half space,the boundary condition of the medium should satisfy the vanished stress on the the debonded region and the continuous stress and displacement on the remainder boundary of the elastic inclusion.The "conjunction" is applied on the common boundary and the debonded region is constructed.A set of infinite algebraic equations to solve this problem are obtained.In the end,numerical examples of the surface displacement about two classical kinds of circular liner used widely in engineering are presented,the influences by the incident wave parameters,the position of debonded region and the depth of circular liners are discussed.
引文
[1]Williams M L.The stresses around a fault or crack indissimilar media[J].Bulletin of the Seismological So-ciety of America,1959,49(2):199-204.
[2]Sih G C.Mechanics of Fracture[M].Leyden:Noord-hof,1973.
[3]Sih G C.Stress distribution near internal crack tipsfor longitudinal shear problems[J].Journal of AppliedMechanics,1965,32(1):51-58.
[4]Loeber J F,Sih G C.Diffraction of antiplane shearwaves by a finite crack[J].Journal of the AcousticalSoceity of America,1968,44(1):90-98.
[5]汪越胜,王铎.SH波对有部分脱胶衬砌的圆形孔洞的散射[J].力学学报,1994,26(4):462-469.(WangYuesheng,Wang Duo.Diffraction of SH-wave by acircular cavity with a particular debonded liner[J].Acta Mechanics Sinica,1994,26(4):462-469.(in Chi-nese))
[6]汪越胜,王铎.剪切波作用下圆弧形界面裂纹的动强度因子[J].固体力学学报,1993,14(4):362-367.(Wang Yuesheng,Wang Duo.Dynamic stress intensi-ty factors of circular arc-shaped interface cracks sub-jected to shear waves[J].Acta Solida Mechanics Sini-ca,1993,14(4):362-367.(in Chinese))
[7]李彤,王国庆,刘殿魁.SH波在含圆形孔洞的半圆形凸起处的散射[J].地震工程与工程振动,2003,23(5):26-31.(Li Tong,Wang Guoqing,Liu Diankui.Scattering of SH-wave by a semi-cylindral hill-likeprotruding with a cavity[J].Earthquake Engineeringand Engineering Vibration,2003,23(5):26-31.(inChinese))
[8]刘殿魁,林宏.浅埋的圆柱形孔洞对SH波的散射与地震动[J].爆炸与冲击,2003,1(1):6-12.(Liu Di-ankui,Lin Hong.Scattering of SH-wave by a shallowburied cylindrical cavity and the ground motion[J].Explosion And Shock Waves,2003,1(1):6-12.(inChinese))
[9]史文谱,刘殿魁,宋永涛.直角平面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.(Shi Wenpu,Liu Diankui,SongYongtao.The Anti-plane Green function of the prob-lem of a fixed rigid circular inclusion in right-angleplane[J].Acta Solida Mechanics Sinica,2006,27(2):207-212.(in Chinese))
[10]刘刚,刘殿魁.SH波入射时浅埋圆孔附近等腰三角形凸起地形的地震动[J].固体力学学报,2007,28(1)60-66.(Liu Gang,Liu Diankui.The ground motion ofan isosceles triangular Hill above a subsurface cavitywith incident SH waves[J].Acta Solida MechanicsSinica,2007,28(1):60-66.(in Chinese))
[2]Sih G C.Mechanics of Fracture[M].Leyden:Noord-hof,1973.
[3]Sih G C.Stress distribution near internal crack tipsfor longitudinal shear problems[J].Journal of AppliedMechanics,1965,32(1):51-58.
[4]Loeber J F,Sih G C.Diffraction of antiplane shearwaves by a finite crack[J].Journal of the AcousticalSoceity of America,1968,44(1):90-98.
[5]汪越胜,王铎.SH波对有部分脱胶衬砌的圆形孔洞的散射[J].力学学报,1994,26(4):462-469.(WangYuesheng,Wang Duo.Diffraction of SH-wave by acircular cavity with a particular debonded liner[J].Acta Mechanics Sinica,1994,26(4):462-469.(in Chi-nese))
[6]汪越胜,王铎.剪切波作用下圆弧形界面裂纹的动强度因子[J].固体力学学报,1993,14(4):362-367.(Wang Yuesheng,Wang Duo.Dynamic stress intensi-ty factors of circular arc-shaped interface cracks sub-jected to shear waves[J].Acta Solida Mechanics Sini-ca,1993,14(4):362-367.(in Chinese))
[7]李彤,王国庆,刘殿魁.SH波在含圆形孔洞的半圆形凸起处的散射[J].地震工程与工程振动,2003,23(5):26-31.(Li Tong,Wang Guoqing,Liu Diankui.Scattering of SH-wave by a semi-cylindral hill-likeprotruding with a cavity[J].Earthquake Engineeringand Engineering Vibration,2003,23(5):26-31.(inChinese))
[8]刘殿魁,林宏.浅埋的圆柱形孔洞对SH波的散射与地震动[J].爆炸与冲击,2003,1(1):6-12.(Liu Di-ankui,Lin Hong.Scattering of SH-wave by a shallowburied cylindrical cavity and the ground motion[J].Explosion And Shock Waves,2003,1(1):6-12.(inChinese))
[9]史文谱,刘殿魁,宋永涛.直角平面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.(Shi Wenpu,Liu Diankui,SongYongtao.The Anti-plane Green function of the prob-lem of a fixed rigid circular inclusion in right-angleplane[J].Acta Solida Mechanics Sinica,2006,27(2):207-212.(in Chinese))
[10]刘刚,刘殿魁.SH波入射时浅埋圆孔附近等腰三角形凸起地形的地震动[J].固体力学学报,2007,28(1)60-66.(Liu Gang,Liu Diankui.The ground motion ofan isosceles triangular Hill above a subsurface cavitywith incident SH waves[J].Acta Solida MechanicsSinica,2007,28(1):60-66.(in Chinese))
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