径向非均匀介质中圆形夹杂的动应力分析

基于复变函数理论,研究了径向非均匀弹性介质中均匀圆夹杂对弹性波的散射问题. 介质的非均匀性体现在介质密度沿着径向按幂函数形式变化且剪切模量是常数. 利用坐标变换法将变系数的非均匀波动方程转为标准亥姆霍兹(Helmholtz) 方程. 在复坐标系下求得非均匀基体和均匀夹杂同时存在的位移和应力表达式. 通过具体算例分析了圆夹杂周边的动应力集中系数(DSCF). 结果表明:基体与夹杂的波数比和剪切模量比,基体的参考波数和非均匀参数对动应力集中有较大的影响. 

DYNAMIC ANALYSIS ON A CIRCULAR INCLUSION IN A RADIALLY INHOMOGENEOUS MEDIUM

Based on the complex function theory, scattering by elastic waves around a homogeneous circular inclusion buried in a radially inhomogeneous elastic medium is investigated in the paper. The inhomogeneity of the medium is assumed that the density depends on the radial distance as a power-law function and the shear modulus is constant. Inhomogeneous wave equation with variable coefficient is converted to the standard Helmholtz equation by using the coordinate transformation. The expressions of displacement and stress fields in complex coordinate are presented due to the existing of both the inhomogeneous base and homogeneous inclusion. The dynamic stress concentration factor (DSCF) around the inclusion is illustrated numerically by examples. Results show that wave number and shear modulus ratios between the base and inclusion, wave number of the base, inhomogeneous parameter have great influence on the dynamic stress concentration.