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利用复变函数法和多极坐标移动技术研究了SH波作用下地表覆盖层与浅埋圆柱形弹性夹杂的相互作用,并给出了圆柱形夹杂周边动应力集中系数的数值结果。首先,为了克服直接构造波函数场的困难,采用一个半径很大的圆形边界来拟合半空间的直边界,因而,具有地表覆盖层的半空间直边界问题就转化成了曲面边界问题,可采用大圆弧假定法求解;其次,借助Helmholtz定理预先写出问题波函数的一般形式解,再利用边界条件并借助复数Fourier-Hankel级数展开将问题化为求解波函数中未知系数的无穷线性代数方程组;最后,截断该无穷代数方程组,以求得该问题的数值结果。分析表明,半空间地表覆盖层的存在,即使其厚度很薄,对入射SH波的散射也具有很大的影响。
The interaction between surface covering and shallow cylindrical elastic inclusions under SH wave action is studied by using the complex function method and the multi-polar coordinate moving technique. The numerical results of dynamic stress concentration factor around the cylindrical inclusion are also given. First, in order to overcome the difficulty of constructing the wave function field directly, a circular boundary with a large radius is used to fit the straight boundary of a half-space. Thus, the problem of straight boundary in a half-space with a surface covering layer transforms into a boundary problem of a surface, It can be solved by the method of big circular arc. Secondly, the general formal solution to the problem wave function is written in advance by means of Helmholtz’s theorem, and then the boundary conditions are used to solve the problem of solving the unknown coefficient in the wave function by using the complex Fourier-Hankel series expansion Linear algebraic equations; Finally, truncate the system of infinite algebra to find the numerical results of the problem. The analysis shows that the existence of half-space surface overburden, even if its thickness is very thin, has a great impact on the scattering of incident SH wave.