半无限空间中稳态P波在衬砌周围的散射

本文采用多级坐标和复变函数方法针对半无限空间中P波在一衬砌周围的散射问题提出了一种近似求解分析方法。具体做法是利用一个半径很大的圆来逼近半空间的直边界，将待解问题转化为全空间中P波在一圆孔和一衬砌周围的共同散射问题。我们预先写出问题波函数的一般形式解，利用边界条件并借助复数傅立叶级数展开把问题化为求解波函数中未知系数的无穷线性代数方程组，进而讨论了衬砌内外边界处动应力集中系数针对不同条件组合的分布和变化情况。算例结果表明：本文方法对于研究与P波（SV波）有关的散射问题是可行的。

Scattering of steady P-wave around a circular lining in half space

The multi polar coordinate and complex function are used to put forward an approximate analysis method for scattering of steady P wave around a circular lining in half space. Here, a circular cavity with large radius is used to replace the straight boundary of the half space. So the problem in this paper will be reduced to scattering of P waves by two cavities. The general solution of the wave functions is given and a system of infinite linear algebraic equations of the problem studied in this paper can be given by means of the complex series expansion technology. Then the variation of the DSCF at inside and outside boundaries of the lining is discussed with different conditions. The results of the given example indicate that the method used in this paper is useful and efficient to the scattering problem of P(SV) waves in which the straight boundary exists.