Critical velocity of a load moving on a beam supported by a foundation of finite depth

In this paper, the critical velocity of a uniformly moving load is analysed. It is assumed that the load is traversing an infinite beam supported by a finite depth foundation under plane strain condition. Analytical solution of the steady state deflection shape is derived. The critical velocity is then extracted by parametric analysis. Results obtained are compared with the previously published results of this author, where simplified plane models of the foundation were used. It is confirmed that there is an interaction between the beam and the foundation and thus the critical velocity is dependent on the mass ratio defined as the square root of the fraction of the foundation mass to the beam mass. For a low mass ratio, the critical velocity approaches the classical formula and for a higher mass ratio, it approaches the lowest wave-velocity of propagation in the foundation. There is only a small difference with respect to the previously published approximate formula for the critical velocity.