RESPONSE OF AN ELASTICALLY SUPPORTED FINITE BEAM TO A MOVING LOAD WITH CONSIDERATION OF THE MASS OF THE FOUNDATION.

The response of a finite beam resting on an elastic foundation to a moving load is studied, taking the effect of the mass of the foundation into account. The foundation is represented as a base consisting of a set of independent rods or linear springs. The solution is formulated by the method of the Laplace integral transformation with respect to time and by the Fourier finite integral transformation with respect to a space variable. As illustrations, a simply supported beam and a clamped beam subjected to a moving concentrated load are treated. The displacement and the bending moment in the beam are calculated for several values of the load velocity and the mass of the foundation, and are plotted as a function of time. The response curves are also compared with those for the massless foundation. It is found that the effect of the mass of the foundation on the beam responses becomes more significant as the load velocity becomes higher.