各向异性介质中有衬砌的非圆形结构与SH波的相互作用*
The Interaction of Plane SH-Waves and Non-Circular Cavity Surfaced with Lining in Anisotropic Media
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摘要: 本文利用复变函数方法求解各向异性介质中有衬砌的非圆形结构与SH波的相互作用问题。各向异性介质可以用来模拟结构周围的地质条件。利用作者在文献[5,7]中的方法决定介质和衬砌结构中的散射波,结合Savin在文献[6]中求解有衬砌结构所采用的对结构轮廓线进行近似处理的方法,并利用结构与介质的连续性条件与衬砌内边界上的边界条件,对问题进行求解。作为算例。本文讨论了在同一种各向异性介质中,两种不同材料组成的正方形有衬砌的结构与SH波的相互作用问题。给出了数值分析结果。Abstract: This is an expand of the complex function method in solving the problem of interaction of plane.SH-waves and non-circular cavity surfaced with linig in anisotropic media.the use the method similar to that incorporated in [2] added with Savin's method for solving stress concentration of non-circular cavity surfaced with lining in elasticity.Anisotropic media can be used ic simulate the conditions of thegeology.The solving proceeding for this problem can be processed conveniently in the manner similar to that introduced in [2].In this paper.as illustrated in example numerical studies have been done for a square cavity surfaced with lining in anisotropic media.
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Key words:
- SH-waves /
- anisotropic media /
- non-circular cavity surfaced with lining
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[1] Y.H.Pao Elastic waves in solids,ASME J.Appl.Mech.,50,4(1983),1152-1746. [2] Liu Diankui and Han Feng,The scattering of plane SH-wave by non-circular cavity in anisotropic media,ASME J.Appl.Mech.(in press) [3] G.N.Savin,Stess Concentration around Holes,1st Ed.(1951),2nd Enlarged Ed.Moscow(1966).(in Russian) [4] Y.H.Pao and C.C.Mow,Diffraction of Elastic Waves and Dynamic Stress Concentrations.Crane and Russak,New York(1973). [5] Liu Diankui,Dynamic stress conception around a circular hole due to SH-wave in anisotropic media.Acta Mechanica Sinica,4,(1988).147-155. [6] Liu Diankui,Gai Bingzhen and Tao Guiyuan,Application of method of complex function to dynamic stress concentration,Wave Motion 4(1982),293-304. [7] Liu Diankui and Han Feng,Scattering of plane SH-waves on cylindrical canyon of arbitrary shape in anisotropic media,Acta.Ytechanica Sinica,6,3(1990),256-266. [8] Liu Diankui and Han Feng,Scattering of plane SH-wave by cylindrical canyon of arbitrary shape,Soil Dyn.and Ear.Eng.,10,5(1991),241-255. [9] Nasser Moeen-Vaziri and M.D.Trifunac,Scattering of plane SH-waves by cylindrical canals of arbitrary shape,Soil Dyn.and Ear.Eng.,4,1(1985),18-23.
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