Influence of horizontal resistance at plate bottom on vibration of plates on elastic foundation under moving loads

The dynamic displacement response of a thin plate, which has horizontal resistance at its bottom, resting on an elastic foundation has been investigated when the system is subjected to a moving load with either constant or harmonic amplitude variations. A distributed load with a constant advance velocity and damping of a linear hysteretic nature for the foundation were considered. Formulations were developed in the transformed field domains of time, space, and moving space, and a double Fourier transform was used to obtain the steady-state response to a moving harmonic load and the response to a moving load of constant amplitude. Analyses were performed: (1) to investigate the effects of various parameters, such as the load velocity, load frequency, and damping, on the deflected shapes, maximum displacements, and critical velocities and frequencies and (2) to examine how the horizontal resistance at the plate bottom affects the vibration. Expressions to predict the critical velocities and frequencies considering the effect of the horizontal resistance were proposed.