Steady-state dynamic response of a gradient elastic half-plane to a load moving on its surface with constant speed.

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]