浅埋相邻多个圆形衬砌与SH波的相互作用
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摘要
利用SH波散射的对称性与多极坐标法,构造了一个可以满足水平地面上应力自由边界条件的浅埋相邻多圆形衬砌对SH波散射的波函数。利用此波函数,将半空间的问题转化成对全空间中的相邻多圆形衬砌的散射问题的求解。该问题又可归结为对一组无穷代数方程组的求解问题,并可利用截断有限项的方法对其进行计算。作为算例,检验了截断计算的精度,给出了当稳态SH波入射时有关浅埋相邻二个圆形衬砌的动应力集中问题的数值结果, 并予以了讨论。
Based upon the symmetry of scattering of SH-wave and the method of multi-polar coordinates system, a scattered wave function is constructed which satisfies the condition of stress free at ground surface caused by multi-faced circular liner at shallow depth impacted by incident steady SH-wave. Using this scattered wave function , the problem can be summarized to scattering of SH-wave by multiple circular liners in whole space. And finally, the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite algebraic equations. As a example, the accuracy of the solution is examined and the numerical results of dynamic stress concentration around two circular liners are given.
Based upon the symmetry of scattering of SH-wave and the method of multi-polar coordinates system, a scattered wave function is constructed which satisfies the condition of stress free at ground surface caused by multi-faced circular liner at shallow depth impacted by incident steady SH-wave. Using this scattered wave function , the problem can be summarized to scattering of SH-wave by multiple circular liners in whole space. And finally, the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite algebraic equations. As a example, the accuracy of the solution is examined and the numerical results of dynamic stress concentration around two circular liners are given.
引文
[1]林皋．地下结构抗震分析综述(上)[J]．世界地震工程,1990,5(2):1 -10．
[2] Pao Y H. Applied mechanics in science and engineering[ J]. Applied Mechanics Review, 1998,51 (2):141-153.
[3]阎盛海．地下结构抗震[M]．大连:大连理工大学出版社,1989．
[4]林宏,刘殿魁．半无限空间中圆形空洞周围SH波的散射[J]．地震 工程与工程振动,2002,22(2):9-16．
[5]王国庆．界面附近相邻多个圆形孔洞对SH波的散射[D]．哈尔滨: 哈尔滨工程大学,2002．
[6]袁晓铭．地表下圆形夹塞区出平面散射对地面运动的影响[J]．地 球物理学报,1996,39(3),375-383．
[7]韩峰,韦扬,刘殿魁．各向异性介质中带衬砌的圆形结构与SH波的 相互作用[J]．应用数学与力学,1995,16(12):1067-1076．
[8] Pao Y H, Mow C C. The Diffraction of elastic waves and dynamic stress concentrations[M]. New York: Crane & Russak, 1973.
[9]周德良,翁智远．弹性半空间中相邻两结构在SH波作用下的动力 响应[J]．固体力学学报,1992,13(3):244-248．
[2] Pao Y H. Applied mechanics in science and engineering[ J]. Applied Mechanics Review, 1998,51 (2):141-153.
[3]阎盛海．地下结构抗震[M]．大连:大连理工大学出版社,1989．
[4]林宏,刘殿魁．半无限空间中圆形空洞周围SH波的散射[J]．地震 工程与工程振动,2002,22(2):9-16．
[5]王国庆．界面附近相邻多个圆形孔洞对SH波的散射[D]．哈尔滨: 哈尔滨工程大学,2002．
[6]袁晓铭．地表下圆形夹塞区出平面散射对地面运动的影响[J]．地 球物理学报,1996,39(3),375-383．
[7]韩峰,韦扬,刘殿魁．各向异性介质中带衬砌的圆形结构与SH波的 相互作用[J]．应用数学与力学,1995,16(12):1067-1076．
[8] Pao Y H, Mow C C. The Diffraction of elastic waves and dynamic stress concentrations[M]. New York: Crane & Russak, 1973.
[9]周德良,翁智远．弹性半空间中相邻两结构在SH波作用下的动力 响应[J]．固体力学学报,1992,13(3):244-248．
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