Critical velocities of a beam on nonlinear elastic foundation under harmonic moving load

The present paper is concerned with the numerical FEM analysis of the dynamic response of a simply-supported Euler-Bernoulli elastic beam resting on a spatially homogeneous nonlinear cubic elastic Winkler foundation subjected to a concentrated moving load. The load moves at a constant velocity along the beam, displaying a harmonic-varying magnitude in time, defined in terms of mean value, amplitude and frequency of oscillation. Parametric analyses are performed to investigate the influence of the moving load parameters on the so-called critical velocities, leading to large displacements, possibly harmful for the structural system. The relationship between critical velocities and moving load parameters is portrayed in appropriate analytical curves, derived from the obtained numerical results, by proposed analytical functional dependencies, with calibrated coefficients. The ensuing outcomes shall reveal practical implications in the description and control of track vibrations induced by high-speed trains, within contemporary railway engineering scenarios, where the critical velocity onset may be lowered down by the effect of the magnitude-varying moving load.