  We consider the problem of the nonlinear response of a Rayleigh beam to the
passage of a train of forces moving with stochastic velocity. The Fourier
transform and the theory of residues is used to estimate the mean-square
amplitude of the beam, while the stochastic averaging method gives the
stationary probability density function of the oscillations amplitude. The
analysis shows that the effect of the load random velocities is highly
nonlinear, leading to a nonmonotonic behavior of the mean amplitude versus the
intensity of the stochastic term and of the load weight. The analytic approach
is also checked with numerical simulations. The effect of loads number on the
system response is numerically investigated.
