Stability and dynamic response of Rayleigh beam–columns on an elastic foundation under moving loads of constant amplitude and harmonic variation

The stability and dynamic response of an infinite Rayleigh beam–column, which considers the effects of the rotary inertia and the axial compressive force, resting on an elastic foundation have been investigated when the system is subjected to moving loads of either constant amplitude or harmonic amplitude variation with a constant advance velocity. Formulations in the transformed field domains of time and moving space were employed, and the response to moving loads of constant amplitude and the steady-state response to moving harmonic loads were obtained using a Fourier transform. Analyses were performed: (1) to examine how the rotary inertia and the axial compression affect the stability and vibration of the system, and (2) to investigate the effects of various parameters, such as the load velocity, load frequency, radius of gyration, and damping, on the deflected shape, maximum displacement, and critical values of the velocity, frequency, and axial compression. Expressions to predict the critical (resonance) velocity, critical frequency, and axial buckling force were proposed. The effect of multiple moving loads was finally examined by considering two moving loads with various values of the load distance and the phase between the loads.