Dynamic models of a railroad track system

A continuum model with microstructure is presented for a railroad track system. The track is represented as a laminated structure with two layers continuously supported by springs and dampers. The differential equations advanced by Sun 24 for a composite system are used in the formulation. Solutions for deflections of the track system subjected to a moving wheel load are obtained in a close form using complex Fourier transforms for both damped and undamped foundations. Comparisons are made with the results obtained from quasi-static models of the track, which simulate the track as a single equivalent homogeneous beam on an elastic foundation with an effective modulus suggested by Voigt. 31 Results of the model are compared with experimental data in limiting cases. Critical velocities are calculated for the track system with conventional rails. The influence of foundation modulus on critical velocity is analysed in some detail. Critical velocities are also computed for an equivalent homogeneous track system using equations advanced by Kerr 10 for a beam. The results of this study agree quite well with those obtained using the continuum model with microstructure.