Due to the inhomogeneity of shear modulus, the constitutive form of the medium becomes more complicated, which increases the difficulty of solving the analytical solution. In this paper, a new form of shear modulus is derived. Meanwhile, the wave number in the medium is also variable. By using the method of complex function and conformal transformation, the problem of dynamic stress concentration around a cylindrical cavity in an infinite inhomogeneous medium is solved. Combined with an auxiliary displacement function and a pair of new mapping functions, in the solving process, the analytical expressions of displacement field and stress field are given. The validity of this method is verified by comparing with the published results. Through numerical results, the distribution of dynamic stress concentration factor around a cylindrical cavity is analyzed under different inhomogeneous parameters and reference wave numbers.

由于剪切模量的不均匀性，介质的本构形式变得更加复杂，增加了解析解的求解难度。本文推导了一种新形式的剪切模量。同时，介质中的波数也是可变的。采用复函数和保角变换的方法，解决了无限不均匀介质中圆柱腔周围的动应力集中问题。结合一个辅助位移函数和一对新的映射函数，在求解过程中，给出了位移场和应力场的解析表达式。通过与已发表的结果进行比较，验证了该方法的有效性。通过数值结果，