NATURAL VIBRATION ANALYSIS OF RAIL TRACK AS A SYSTEM OF ELASTICALLY COUPLED BEAM STRUCTURES ON WINKLER FOUNDATION

An analytical model for analyzing the vertical free vibration of a rail track is presented. The track structure is represented as a system of elastically coupled beam structures resting on a Winkler foundation. The rail and the tie beams are described by any combination of the two existing beam theories, the Bernoulli-Euler type, and the Timoshenko type, while the rail is assumed to be periodically supported at discrete points on cross-track tie beams. A generalized track element, which consists of a rail span (beam segment), two adjacent ties, and the coupling spring stiffnesses, is established to discretize the track system into identical units. A concept of an equivalent frequency-dependent spring coefficient for the rail support system is introduced to formulate the dynamic stiffness matrix of the track element. Solutions are provided for the natural frequencies of the track and the associated mode shapes of the rail and the ties under transversely (cross-track) symmetric vibration. The free vibration results are used to obtain the dynamic receptance response of a typical field track and to compare them with an existing model and field experimental data.