Response of a beam on an inertial foundation to a traveling load

The response of a Bernoulli-Euler beam supported by a Winkler-type elastic foundation with inertia and subjected to a moving load is investigated. Steady-state solutions are determined for an undamped and linearly damped beam-foundation system. The effects on the response of load velocity, foundation mass, and damping are studied. For the undamped system, it is well known that the response grows without bound as a certain critical velocity is approached. It is shown that the effect of foundation mass is to reduce the critical velocity and to increase the peak deflection. The increase in peak deflection becomes more pronounced as the critical velocity is approached. As in the case of massless foundation, the deflection wave is observed to be symmetric with respect to the load. When damping is introduced, the deflection wave loses its symmetry, and the peak deflection is reduced. Results for both cases are given in graphical form.