基于线弹性动力学理论，结合坐标变换，建立了移动荷载作用下非均匀弹性半平面地基的动力控制方程，利用半解析法研究了移动荷载作用下二维非均匀地基的动力响应问题。采用傅里叶（Fourier）级数展开，假设了响应函数的级数形式，通过理论推导获得了剪切模量随深度任意变化的非均匀地基在移动荷载作用下各物理量的解析表达式。考虑土体的剪切模量沿厚度方向按幂函数梯度变化，通过数值算例分析并讨论了地基非均匀参数、荷载移动速度以及地基表面的剪切模量等对地基力学响应的影响规律，并与均质地基的计算结果进行了比较。数值结果表明：地基中各点的竖向位移随着土体表面剪切模量和表征土体非均匀性的梯度因子的增大而减小，随着荷载移动速度的增大而增大。在移动荷载作用下，非均匀地基与均匀地基的动力响应有着显著的区别。

Based on the theory of linear elastodynamics, and combined with the coordinate transformation, the dynamic governing equations for a half-plane inhomogeneous subgrade are developed. The dynamic response of a two-dimensional inhomogeneous subgrade subjected to moving loads is analyzed based on a semi-analytical method. Using Fourier series expansion, and assuming the series form of response function, the analytical expressions of various physical quantities are developed for the inhomogeneous subgrade subjected to moving loads, in which the shear modulus can arbitrarily change with depth. Assuming the shear modulus has an exponential distribution with the thickness, a parametric study is presented to illustrate the influence of the foundation soil inhomogeneity and load moving velocity as well as shear modulus at subgrade surface on the dynamical response of foundation soils. The calculated results are compared with the responses of a homogeneous subgrade, showing that the vertical displacement of soil decreases with the increase of the shear modulus at the surface of subgrade and the inhomogeneous gradient index, and increases with the increase of the load moving velocity. Under a moving load, the dynamic responses of inhomogeneous subgrade are significantly different from that of homogeneous subgrade.