含有部分脱胶的浅埋圆夹杂对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柱形弹性夹杂对SH波的散射与地震动问题。在圆形弹性夹杂中构造一个满足脱胶部分应力自由的驻波函数,将其展开为含有一个待定系数的Fourier级数。在半空间中,介质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,从而建立起求解该问题的无穷代数方程组。最后,给出了地表位移的数值结果。给果表明,入射波参数、脱胶位置、弹性夹杂参数以及埋深对地表位移都有一定程度的影响。
The scattering of SH-waves by a shallow buried cylindrical elastic inclusion with a partially debonded curve in half space is studied by function of complex variable method.Firstly,the standing wave function in the cylindrical elastic inclusion is constructed,where satisfies that the stress on the debonded curve is zero.Then the function is generated into the Fourier series.In the half space,the boundary condition of the medium satisfies that the stress on the debonded curve is zero and the stress and displacement on the common border are continuous with the elastic inclusion.Then,a set of infinite algebraic equations to solve this problem can be obtained.In the end,numerical examples of the surface displacement are presented.The results indicates that the surface displacement could be influenced by the incident wave parameters,the position of debonded curve,the parameters of elastic inclusion and the depth of the buried inclusion to some extent.
The scattering of SH-waves by a shallow buried cylindrical elastic inclusion with a partially debonded curve in half space is studied by function of complex variable method.Firstly,the standing wave function in the cylindrical elastic inclusion is constructed,where satisfies that the stress on the debonded curve is zero.Then the function is generated into the Fourier series.In the half space,the boundary condition of the medium satisfies that the stress on the debonded curve is zero and the stress and displacement on the common border are continuous with the elastic inclusion.Then,a set of infinite algebraic equations to solve this problem can be obtained.In the end,numerical examples of the surface displacement are presented.The results indicates that the surface displacement could be influenced by the incident wave parameters,the position of debonded curve,the parameters of elastic inclusion and the depth of the buried inclusion to some extent.
引文
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[4]尤红兵,梁建文.层状半空间中洞室对入射平面SV波的散射[J].岩土力学,2006,27(3):383-388.YOU Hong-bing,LIANG Jian-wen.Scattering of plane SV waves by a cavity in a layered half-space[J].Rock and Soil Mechanics,2006,27(3):383-388.
[5]梁建文,李艳恒,LEE V W.地下洞室群对地面运动影响问题的级数解答:SH波入射[J].岩土力学,2006,27(10):1663-1672.LIANG Jian-wen,LI Yan-heng,LEE V W.A series solution for surface motion amplification due to underground group cavities:incident SH waves[J].Rock and Soil Mechanics,2006,27(10):1663-1672.
[6]杨彩红,梁建文,张郁山.多层沉积凹陷地形对平面SH波散射问题的解析解[J].岩土力学,2006,27(12):2191-2196.YANG Cai-hong,LIANG Jian-wen,ZHANG Yu-shan.Analytical solution of scattering of plane SH waves around a canyon with multi-layered alluvia[J].Rock and Soil Mechanics,2006,27(12):2191-2196.
[7]刘殿魁,王国庆.浅埋圆形孔洞附近的半圆形凸起对SH波的散射[J].力学学报,2006,3(2):209-218.LIU Dian-kui,WANG Guo-qing,Antiplane SH-deformation of a semi-cylindrical hill above a subsurface cavity[J].Acta Mechanics Sinica,2006,3(2):209-218.
[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 Dian-kui,LIN Hong.Scattering of SH-waves by a shallow buried cylindrical cavity and the ground motion[J].Explosion And Shock Waves,2003,1(1):6-12.
[2]SIH G C.Mechanics of Fracture(vol.1)[M].Leyden:Noordhoff,1973.
[3]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 Yue-sheng WANG Duo.Dynamic stress intensity factors of circular arc-shaped interface cracks subjected to shear waves[J].Acta Solida Mechanics Sinica,1993,14(4):362-367.
[4]尤红兵,梁建文.层状半空间中洞室对入射平面SV波的散射[J].岩土力学,2006,27(3):383-388.YOU Hong-bing,LIANG Jian-wen.Scattering of plane SV waves by a cavity in a layered half-space[J].Rock and Soil Mechanics,2006,27(3):383-388.
[5]梁建文,李艳恒,LEE V W.地下洞室群对地面运动影响问题的级数解答:SH波入射[J].岩土力学,2006,27(10):1663-1672.LIANG Jian-wen,LI Yan-heng,LEE V W.A series solution for surface motion amplification due to underground group cavities:incident SH waves[J].Rock and Soil Mechanics,2006,27(10):1663-1672.
[6]杨彩红,梁建文,张郁山.多层沉积凹陷地形对平面SH波散射问题的解析解[J].岩土力学,2006,27(12):2191-2196.YANG Cai-hong,LIANG Jian-wen,ZHANG Yu-shan.Analytical solution of scattering of plane SH waves around a canyon with multi-layered alluvia[J].Rock and Soil Mechanics,2006,27(12):2191-2196.
[7]刘殿魁,王国庆.浅埋圆形孔洞附近的半圆形凸起对SH波的散射[J].力学学报,2006,3(2):209-218.LIU Dian-kui,WANG Guo-qing,Antiplane SH-deformation of a semi-cylindrical hill above a subsurface cavity[J].Acta Mechanics Sinica,2006,3(2):209-218.
[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 Dian-kui,LIN Hong.Scattering of SH-waves by a shallow buried cylindrical cavity and the ground motion[J].Explosion And Shock Waves,2003,1(1):6-12.
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