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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 elastic dynamics and combined with coordinate transformation, the dynamic governing equation of a non-uniform elastic half-plane foundation under moving loads is established. The dynamic response of a two-dimensional non-uniform foundation under moving loads is studied by semi-analytical method. By using Fourier series expansion, the order form of the response function is assumed. The analytic expressions of the physical quantities of the nonhomogeneous foundation with varying shear modulus varying with depth under the action of moving load are obtained through theoretical derivation. Considering that the shear modulus of the soil varies with the power function gradient along the thickness direction, the influence laws of the non-uniform parameters, the load moving velocity and the shear modulus of the ground surface on the mechanical response of the foundation are analyzed and discussed through numerical examples. The results are compared with those of the homogeneous foundation. The numerical results show that the vertical displacement of each point in the foundation decreases with the increase of the shear modulus of soil surface and the gradient factor that characterizes the heterogeneity of soil mass, and increases with the increase of load moving velocity. Under the action of moving loads, there is a significant difference between the dynamic responses of the non-uniform foundation and the uniform foundation.