SH波入射多个半圆形谷地浅埋圆孔的动力分析
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摘要
应用辅助函数的思想,通过复变函数和多级坐标的方法给出了SH波入射条件下多个半圆形沉积谷地附近多个浅埋圆形孔洞动力分析问题的解答。求解过程中将整个求解区域划分成两部分来处理:区域I为多个半圆形沉积谷地,区域II为多个浅埋圆形孔洞附近带多个半圆形凹陷的半无限弹性空间。在区域I和II中分别构造位移解,并在二个区域的“公共边界”上实施位移、应力的连续条件,建立起求解该问题的无穷代数方程组。最后,给出了分析例题和数值结果,并对其进行了讨论。
Dynamic response of multiple shallow-embedded cylindrical cavities below semi-cylindrical alluvial valleys to incident SH waves is studied by using complex function.The model is divided into two parts,and two solutions are constructed in the domains,respectively.One is standing waves, while another is the scattering by multiple semi-cylindrical alluvial valleys and multiple subsurface circular cavities.Each of the two functions satisfies the zero-stress condition at the horizontal boundary.By employing displacement and stress continuity condition on the interface,the problem to be solved can be reduced to solving a set of infinite linear algebraic equations.Finally,the computational results of dynamic stress concentration factors and some discussions are provided.
Dynamic response of multiple shallow-embedded cylindrical cavities below semi-cylindrical alluvial valleys to incident SH waves is studied by using complex function.The model is divided into two parts,and two solutions are constructed in the domains,respectively.One is standing waves, while another is the scattering by multiple semi-cylindrical alluvial valleys and multiple subsurface circular cavities.Each of the two functions satisfies the zero-stress condition at the horizontal boundary.By employing displacement and stress continuity condition on the interface,the problem to be solved can be reduced to solving a set of infinite linear algebraic equations.Finally,the computational results of dynamic stress concentration factors and some discussions are provided.
引文
[1]TrifunacM D.Surface motion of a sem i-cylindrical alluvial valley for incident plane SH waves[J].Bu lletin of the Seismological Society ofAm eri-ca,1971,61(6):1755-1770.
[2]W ong H L,TrifunacM D.Surface motion of a sem i-elliptical alluvial valley for incident plane SH waves[J].Bu lletin of the Seismological SocietyofAm erica,1974,64(5):1389-1408.
[3]Tordovoska M,Lee V W.Surface motion of a shallow circu lar alluvial valleys for incident plane SH waves:analytical solution[J].Soil DynamEarthq Eng,1991,4:192-200.
[4]Yuan X iaom ing,L iao Zhenpeng.Scattering of plane SH waves by a cylindrical alluvial valley of circu lar arc cross section[J].Earthq Eng StrucDynam,1995,24:1303-1313.
[5]刘殿魁,王艳,陈志刚.SH波垂直入射时半圆形凸起附近的浅埋圆形衬砌结构的动力分析[A].第四届全国工程结构安全防护学术交流论文集[C].2002.
[6]梁建文,严林隽,Lee V W.圆弧形层状沉积谷地对入射平面P波的散射解析解[J].地震学报,2001,23(2):167-184.
[7]梁建文,严林隽,Lee V W.圆弧形凹陷地形表面覆盖层对入射平面SV波的影响[J].地震学报,2001,23(6):622-636.
[8]梁建文,严林隽,李军伟,Lee V W.圆弧形沉积河谷场地在平面P波入射下的响应[J].岩土力学,2001,22(2):138-143.
[9]袁晓铭,廖振鹏.任意圆弧形凸起地形对平面SH波的散射[J].地震工程与工程振动,1996,16(2):1-13.
[10]W ang G Q,L iu D K.Scattering of SH-wave by mu ltiple circu lar cavities in half space[J].Earthquake engineering and Engineering vibration,2002,1(1):36-44.
[2]W ong H L,TrifunacM D.Surface motion of a sem i-elliptical alluvial valley for incident plane SH waves[J].Bu lletin of the Seismological SocietyofAm erica,1974,64(5):1389-1408.
[3]Tordovoska M,Lee V W.Surface motion of a shallow circu lar alluvial valleys for incident plane SH waves:analytical solution[J].Soil DynamEarthq Eng,1991,4:192-200.
[4]Yuan X iaom ing,L iao Zhenpeng.Scattering of plane SH waves by a cylindrical alluvial valley of circu lar arc cross section[J].Earthq Eng StrucDynam,1995,24:1303-1313.
[5]刘殿魁,王艳,陈志刚.SH波垂直入射时半圆形凸起附近的浅埋圆形衬砌结构的动力分析[A].第四届全国工程结构安全防护学术交流论文集[C].2002.
[6]梁建文,严林隽,Lee V W.圆弧形层状沉积谷地对入射平面P波的散射解析解[J].地震学报,2001,23(2):167-184.
[7]梁建文,严林隽,Lee V W.圆弧形凹陷地形表面覆盖层对入射平面SV波的影响[J].地震学报,2001,23(6):622-636.
[8]梁建文,严林隽,李军伟,Lee V W.圆弧形沉积河谷场地在平面P波入射下的响应[J].岩土力学,2001,22(2):138-143.
[9]袁晓铭,廖振鹏.任意圆弧形凸起地形对平面SH波的散射[J].地震工程与工程振动,1996,16(2):1-13.
[10]W ang G Q,L iu D K.Scattering of SH-wave by mu ltiple circu lar cavities in half space[J].Earthquake engineering and Engineering vibration,2002,1(1):36-44.
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