本文采用多极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 In this paper, a method of approximate solution to the scattering problem of P wave in a semi-infinite space around a lining is proposed by means of multi-polar coordinates and complex variable functions. The method is to use a circle with large radius to approach the straight boundary of a half-space and transform the problem to be solved into the common scattering problem of P-wave in a full space around a circular hole and a lining. We first write out the general form solution of the wave function of the problem, and use the boundary conditions and complex Fourier series expansion to solve the problem as infinite linear algebraic equations for solving unknown coefficients in the wave function, and then discuss the dynamic stress concentration coefficient According to the distribution of different conditions and changes in the situation. The results show that the proposed method is feasible for the study of scattering problems related to P waves (SV waves)