Vibrations of a beam on elastic foundation II

Abstract

In an earlier paper, the equations describing the vibrations of a beam on elastic foundation under the action of an alternating force whose point of application moves along the beam was solved by the author, neglecting damping. The effect of damping is taken into account in the present work, and explicit solutions, valid for all frequencies and velocities of the applied force, are obtained. In qualitative features the most obvious difference from the undamped case is that, for non-zero velocity, the displacements of the beam are no longer symmetric about the instantaneous position of the applied force, but are greater behind than ahead of this position.