Unified Approach for Beams on Elastic Foundations under Moving Loads

Abstract

This paper describes a simple unified procedure, based on the fast Fourier transform (FFT) technique, for analyzing the steady‐state response of an infinitely long beam supported on an arbitrary linear elastic, damped foundation and subjected to moving oscillatory loads. As an application, the procedure is used to analyze the response of a simplified model of railroad track; the base is idealized either as a Kelvin model, or as a two‐layer Vlasov model for an improved representation of the actual track. For the limiting static problem the results are compared with those from experiments and from a more realistic model (GEOTRACK); agreement between the various results is reasonable, despite the simplicity of the Kelvin and Vlasov models. A parametric study is conducted to assess the significance of system parameters such as the velocity and the frequency of the moving load and the stiffness and damping characteristics of the foundation on the system response. Response quantities evaluated include beam deflections, bending moments, and contact pressure as well as the energy dissipated within the foundation.