SH波对三角形凸起与半圆形凹陷地形的地震动
|
摘要
利用复变函数法与多极坐标法对中间是半圆凹陷、一边是斜三角形凸起和一边是等腰三角形凸起的组合地形对SH波的散射问题进行研究。首先将求解区域分为3个部分,再分别构造不同区域满足边界条件的驻波解,并在公共边界实施"契合",并建立满足半圆形凹陷表面应力自由边界条件的无穷代数方程组。最后通过具体算例分析不同参数对三角形凸起与半圆形凹陷相连地形地震动的影响。
The problem of SH-waves scattering by an oblique triangle hill,a isosceles triangle hill and a semi-cylindrical canyon is studied by using the methods of complex function and multi-polar coordinate.The solution domain is divided into 3 parts,and then displacement solutions of standing waves that meet the boundary conditions are constructed in the three regions respectively.The three domains were conjoined to satisfy the "conjunction" condition and,and then a set of infinite algebraic equations about the problem to satisfy the boundary condition of semi-cylindrical canyon is obtained.Lastly,numerical examples are given to show the influence of different parameters on the ground motion of the hills and the canyon.
The problem of SH-waves scattering by an oblique triangle hill,a isosceles triangle hill and a semi-cylindrical canyon is studied by using the methods of complex function and multi-polar coordinate.The solution domain is divided into 3 parts,and then displacement solutions of standing waves that meet the boundary conditions are constructed in the three regions respectively.The three domains were conjoined to satisfy the "conjunction" condition and,and then a set of infinite algebraic equations about the problem to satisfy the boundary condition of semi-cylindrical canyon is obtained.Lastly,numerical examples are given to show the influence of different parameters on the ground motion of the hills and the canyon.
引文
[1]Trifunac MD.Surface motion of a semi-cylindrical alluvial valley for incident plane SHwaves[J].Bull Seism Soc Am.,1971,61(2):1755-1770.
[2]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.
[3]Liu D K,Han F.Scattering of plane SH-waves by cylindrical canyon of arbitrary shapes in anisotropic media[J].Acta Mechanica Sinica,1990,6(3):256-266.
[4]杜永军,刘殿魁,赵启承,等.SH波入射时等腰三角形与半圆形凸起地形的地震动[J].世界地震工程,2009,25(3):167-174.
[5]吕晓棠,杨在林,刘殿魁.SH波对浅埋圆柱形弹性夹杂附近多个半圆形凸起的散射[J].世界地震工程,2009,25(2):114-119.
[6]吕晓棠,刘殿魁.SH波入射时半圆形凸起与凹陷地形的地震动[J].地震工程与工程振动,2006,26(5):14-20.
[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,2006,38(2):209-218.
[8]Nazaret D,Lee VW,Liang J W.Antiplane deformations around arbitrary-shaped canyons on a wedge-shape half space:moment method solutions[J].Journal of Earthquake Engineering and Engineering Vibration,2003,2(2):281-287.
[2]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.
[3]Liu D K,Han F.Scattering of plane SH-waves by cylindrical canyon of arbitrary shapes in anisotropic media[J].Acta Mechanica Sinica,1990,6(3):256-266.
[4]杜永军,刘殿魁,赵启承,等.SH波入射时等腰三角形与半圆形凸起地形的地震动[J].世界地震工程,2009,25(3):167-174.
[5]吕晓棠,杨在林,刘殿魁.SH波对浅埋圆柱形弹性夹杂附近多个半圆形凸起的散射[J].世界地震工程,2009,25(2):114-119.
[6]吕晓棠,刘殿魁.SH波入射时半圆形凸起与凹陷地形的地震动[J].地震工程与工程振动,2006,26(5):14-20.
[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,2006,38(2):209-218.
[8]Nazaret D,Lee VW,Liang J W.Antiplane deformations around arbitrary-shaped canyons on a wedge-shape half space:moment method solutions[J].Journal of Earthquake Engineering and Engineering Vibration,2003,2(2):281-287.
版权所有：© 2023 中国地质图书馆 中国地质调查局地学文献中心