The problem of determining the dynamic response of a granular elastic half-space soil medium to a rectangular load moving on its surface is determined analytically. The granular material is modeled as a gradient elastic solid with two material constants in addition to the two classical elastic moduli. These material constants with dimensions of length are the micro-stiffness g and the micro-inertia h coefficients. The rectangular load is uniformly distributed of constant magnitude and moves with constant speed. The resulting three partial differential equations of motion are of the fourth order with respect to the horizontal x, y, and vertical z coordinates and of second order with respect to time t. These equations are solved with the aid of double complex Fourier series involving x, y, t, and the load velocity, which reduce them to a system of three ordinary differential equations of the fourth order with respect to z, which can be easily solved. Use of appropriate classical and non-classical boundary conditions can lead to the solution of the problem. The so obtained solution is used to easily assess by parametric studies the effects of the microstructural parameters g and h as well as the moving load velocity on the various response quantities.

确定粒状弹性半空间土壤介质对其表面移动的矩形载荷的动力响应问题进行了解析确定。除了两个经典的弹性模量之外，颗粒材料被建模为具有两个材料常数的梯度弹性固体。这些具有长度尺寸的材料常数是微刚度g和微惯量h系数。矩形载荷均匀分布，大小恒定，并以恒定速度移动。得到的三个运动偏微分方程相对于水平x、y和垂直z坐标为四阶，相对于时间为二阶吨。这些方程借助涉及x、y、t和负载速度的双复傅立叶级数求解，将它们简化为三个关于z的四阶常微分方程组，可以很容易地求解。使用适当的经典和非经典边界条件可以解决问题。如此获得的解决方案用于通过参数研究轻松评估微观结构参数g和h以及移动负载速度对各种响应量的影响。