Dynamic response of a beam on a frequency-independent damped elastic foundation to moving load

Abstract

The dynamic displacement response of an infinitely long beam on an elastic foundation with frequency-independent linear hysteretic damping subjected to a constant amplitude or a harmonic moving load was investigated. The advance velocity was assumed to be constant. Formulations were developed in the transformed field domain using (i) a Fourier transform in moving space for moving loads of constant amplitude, (ii) a double Fourier transform in time and moving space for moving loads of arbitrary amplitude variation or to include the transient due to the initial application of the load for moving harmonic loads, and (iii) a Fourier transform in moving space for the steady-state response to moving harmonic loads. The effects of velocity, damping, loaded length, and load frequency on the deflected shape and the maximum displacement were investigated. The critical (resonant) velocities and frequencies were obtained by analyses, and expressions to find them were suggested.Key words: beam on elastic foundation, damping, Fourier transform, frequency, harmonic load, moving load, transformed field, velocity.