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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. [ABSTRACT FROM AUTHOR]

The problem of determining the steady-state dynamic response of a granular elastic half-plane to a load moving on its surface is solved analytically. The granular material is modeled as a gradient elastic solid with one material constant with length dimensions in addition to the two classical elastic moduli. The load is uniformly distributed of constant magnitude and moves with constant speed. The resulting two partial differential equations of motion are of the sixth order with respect to the horizontal x and vertical y coordinates and of the second order with respect to time t. These equations are solved with the aid of complex Fourier series involving x and t, which reduce them to a system of two ordinary differential equations, which can be easily solved. The so-obtained solution is used to easily assess the microstructural effect on the various response quantities through parametric studies. [ABSTRACT FROM AUTHOR]