Steady-state displacements of a beam on an elastic half-space due to a uniformly moving constant load

The steady-state displacements of an Euler-Bernoulli beam on an elastic half-space due to a uniformly moving constant load are determined using the concept of the equivalent stiffness of the half-space. The displacements are calculated for four different cases of beam and half-space parameters. The displacements in each case are derived for five relevant load velocities. The lowest is small with respect to the shear (S)-wave velocity in the half-space, the subsequent velocities are near the lowest critical velocity, between the critical velocity and the Rayleigh (R)-wave velocity, between the R-wave and S-wave velocity and larger than S-wave velocity. The beam displacement under the load is also determined for each case for all load velocities. Near the critical velocity the effect of an external viscous damping along the beam on the displacement under the load is studied.