Vibration and stability of axial loaded beams on elastic foundation under moving harmonic loads

The vibration and stability of an infinite Bernoulli–Euler beam resting on a Winkler-type elastic foundation have been investigated when the system is subjected to a static axial force and 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 and moving space, and a 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 shape, maximum displacement, and critical values of the velocity, frequency, and axial force, and (2) to examine how the axial force affects the vibration and stability of the system. Expressions to predict the critical (resonance) velocity, critical frequency, and axial buckling force were proposed.