SH波对覆盖层下浅埋圆孔和圆夹杂的散射

利用复变函数法和波函数展开法给出了具有地表覆盖层的弹性半空间内圆形孔洞和圆柱形夹杂在稳态SH波作用下动应力集中问题的解。根据SH波散射的衰减特性,该问题采用大圆弧假定法求解,利用半径很大的圆来拟合地表覆盖层的直边界,将具有地表覆盖层的半空间直边界问题转化为曲面边界问题。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,截断该无穷代数方程组可求得该问题的近似解析解。最后,通过算例讨论了地表覆盖层及圆孔对浅埋圆柱形夹杂动应力集中的影响。结果表明,覆盖层刚度和厚度的变化及圆孔的存在可显著改变圆夹杂周边动应力集中的分布。

SCATTERING OF SH-WAVE BY SUBSURFACE CIRCULAR CAVITIES AND INCLUSIONS IN A LAYERED HALF-SPACE

The solution to the dynamic stress concentration of circular cavities and inclusions subject to SH-Wave in an elastic half-space covered with an elastic layer is attained in this study, using the complex function method and the wave function expansion method. According to the attenuation characteristics of SH-Wave scattering, the problem is attempted by using the large-arc assumption method, in which a circular boundary of a large radius is used to approximate the straight boundary of the surface layer to transform the original problem to a surface boundary problem. With the theory of Helmholtz, the general solution of the Biot’s wave function is obtained. Subsequently, infinite linear algebraic equations with unknown coefficients are formulated using the Fourier-Hankel series expansion and boundary conditions, and the approximate analytic solution is derived by truncating the equations. Finally, the dynamic stress concentration factor around the circular inclusion is discussed in a numerical example. Results show that different stiffness and thickness of the surface layer and the existence of cavities can remarkably change the dynamic stress concentration distribution around circular inclusions.