直角域非等腰三角形凸起对SH波的散射与地震动
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摘要
采用复变函数及移动坐标方法给出了SH波对直角域非等腰三角形凸起散射问题的解析解答。首先,采用"分区"的思想,将求解模型划分为两个区域,区域Ⅰ为含有半圆形弧底的非等腰三角形凸起,区域Ⅱ为含有半圆形凹陷的直角域。求解本文问题的关键在于构造满足非等腰三角形两斜边应力为零的驻波解答和构造满足直角域边界应力为零的散射波解答。其次,根据"公共边界"上应力、位移连续性条件建立无穷代数方程组,并截断有限项求解。最后,给出了地表位移幅值的具体算例。结果表明:入射角度,入射波数以及直角域垂直边界都对地表位移幅值有影响。
The analytical solution to the problem of scattering of SH-wave induced by scalene triangular hill on a right-angle field was given by using the methods of complex function and moving coordinate system.Firstly,the solution model was divided into two domains,domain I was a scalene triangular hill containing a semi-circular bottom,domain II was a right-angle field containing a seim-circular hollow.The key was to construct the standing wave function satisfying zero-stress conditions at the scalene triangular wedges and the scattering wave functions satisfying stress free boundary conditions at the boundaries of the right-angle field,respectively.Secondly,based on the conditions of displacement continuity and stress continuity at the "common border" of the domains,a series of infinite algebraic equations were built and solved with truncation.Finally,some examples for amplitude of displacement on the surface were given.Numerical results showed that amplitude of displacement on the surface is influenced by incident angle,incident wave number and vertical boundary of the right-angle field.
The analytical solution to the problem of scattering of SH-wave induced by scalene triangular hill on a right-angle field was given by using the methods of complex function and moving coordinate system.Firstly,the solution model was divided into two domains,domain I was a scalene triangular hill containing a semi-circular bottom,domain II was a right-angle field containing a seim-circular hollow.The key was to construct the standing wave function satisfying zero-stress conditions at the scalene triangular wedges and the scattering wave functions satisfying stress free boundary conditions at the boundaries of the right-angle field,respectively.Secondly,based on the conditions of displacement continuity and stress continuity at the "common border" of the domains,a series of infinite algebraic equations were built and solved with truncation.Finally,some examples for amplitude of displacement on the surface were given.Numerical results showed that amplitude of displacement on the surface is influenced by incident angle,incident wave number and vertical boundary of the right-angle field.
引文
[1]Trifunac M D.Scattering of plane SH-waves by a semi-cylindrical canyon[J].Earthquake Engineering and StructureDynamic,1972,1(3):267-281.
[2]Lee V W,Manoogian M E.Surface motion above an arbitraryshape underground cavity for incident SH wave[J].EuropeanEarthquake Engineering,1995,8(1):3-11.
[3]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.
[4]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.
[5]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.
[6]刘刚,刘殿魁.SH波对浅埋圆形弹性夹杂附近任意三角形凸起地形的散射[J].应用力学学报,2007,24(3):373-379.
[7]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.
[8]邱发强,王慧文,王雪.SH波入射时非等腰三角形结构与基础相互作用[J].哈尔滨工业大学学报,2010,42(4):634-638.
[9]邱发强,刘殿魁.SH波对等腰三角形凸起地形散射问题中的驻波函数[J].哈尔滨工程大学学报,2007,28(5):525-528.
[10]折勇,齐辉,杨在林.SH波对直角平面区域内圆形孔洞的散射与地震动[J].应用力学学报,2008,25(3):392-397.
[11]邱发强.SH波对三角形凸起及其附近浅埋圆孔的散射[D].哈尔滨:哈尔滨工程大学,2006,53-58.
[2]Lee V W,Manoogian M E.Surface motion above an arbitraryshape underground cavity for incident SH wave[J].EuropeanEarthquake Engineering,1995,8(1):3-11.
[3]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.
[4]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.
[5]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.
[6]刘刚,刘殿魁.SH波对浅埋圆形弹性夹杂附近任意三角形凸起地形的散射[J].应用力学学报,2007,24(3):373-379.
[7]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.
[8]邱发强,王慧文,王雪.SH波入射时非等腰三角形结构与基础相互作用[J].哈尔滨工业大学学报,2010,42(4):634-638.
[9]邱发强,刘殿魁.SH波对等腰三角形凸起地形散射问题中的驻波函数[J].哈尔滨工程大学学报,2007,28(5):525-528.
[10]折勇,齐辉,杨在林.SH波对直角平面区域内圆形孔洞的散射与地震动[J].应用力学学报,2008,25(3):392-397.
[11]邱发强.SH波对三角形凸起及其附近浅埋圆孔的散射[D].哈尔滨:哈尔滨工程大学,2006,53-58.
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