【作者】 韩刘；

【导师】 齐辉；

【作者基本信息】 哈尔滨工程大学 ， 固体力学， 2009， 硕士

【摘要】 本文研究了带有覆盖层的半无限空间中圆形夹杂对SH波的散射问题。利用复变函数法和多极坐标移动技术讨论了带有覆盖层的半空间内浅埋圆形夹杂对稳态任意方向入射平面SH波的散射问题。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数值结果。最后,通过算例来讨论地表覆盖层对浅埋圆形夹杂动应力集中的影响。结果表明,半空间地表覆盖层的存在,即使厚度很薄,对入射SH波的散射也具有很大影响,覆盖层刚度和厚度的变化可显著改变浅埋夹杂周边动应力集中系数的分布。更多还原

【Abstract】 The scattering of SH-wave by subsurface circular inclusions in a layered elastic half-space is studied in this paper. The problem of the scattering of SH-wave by a subsurface circular inclusion in a layered elastic half-space is investigated based on the complex function method and wave function expansion method for arbitrary incident angle. According to the attenuation characteristics of SH-wave, the solution of scattering of SH-wave was given by a circular inclusion embedded in a layered half-space with an almost flat circular boundary to approximate the straight boundary of surface elastic layer. The general solution of the Biot’s wave function is given using the theory of Helmholtz and a system of infinite linear algebraic equations of the present problem can be given by means of the complex series expansion technology and the boundary conditions of the problem. Finally, the dynamic stress concentration factors around the circular inclusion and the ground motion are discussed in numerical examples. The calculation results show that the existence of a surface layer on a half-space, even if it is very thin, has great influence on incident plane SH-wave. The variation of stiffness and thickness of the surface layer can remarkably change the dynamic behavior of circular inclusion.更多还原