Dynamics of beams on non-uniform nonlinear foundations subjected to moving loads

•A FE formulation is developed for beams on elastic foundations under moving loads.•Critical velocities are determined for beams on uniform or non-uniform foundations.•The effects of the foundation’s stiffness and damping are investigated.•This study generalizes the analyses performed recently by other authors. This paper presents a study on the dynamic response of beams on nonlinear elastic foundations, subjected to moving loads. The effects of the load’s intensity and velocity and of the foundation’s stiffness are investigated. Critical velocities are determined for beams on uniform foundations or foundations composed of two sub-domains with different values of stiffness, with or without viscous damping. In the case of non-uniform linear foundations, a very good agreement is obtained between the results of the model and available analytical solutions. The goal of this study is to generalize, for more realistic foundation behaviors, the analyses obtained by other authors.