Buckling and vibration of a plate on elastic foundation subjected to in-plane compression and moving loads

The stability and dynamic displacement response of an infinite thin plate resting on a Winkler-type or a two-parameter elastic foundation have been investigated when the system is subjected to in-plane static compressive forces and a distributed load moving with a constant advance velocity. The amplitude of the moving load was assumed to be either constant or of harmonic variation and damping of a linear hysteretic nature for the foundation were considered. Formulations in the transformed field domains of time, space, and moving space were employed. The steady-state response to a moving harmonic load and the response to a moving load of constant amplitude were obtained using a double Fourier transform. Analyses were performed: (i) to investigate the effects of various parameters, such as the load velocity, load frequency, and damping, on the deflected shapes, maximum displacements, and critical values of the velocity, frequency, and in-plane compression, and (ii) to examine how the in-plane compression affects the stability and vibration of the system. Expressions to predict the critical (resonance) velocity, critical frequency, and in-plane buckling force were proposed.