Modeling infinitely long flexible railroad tracks using moving modes and Krylov subspaces techniques

This paper presents a method to model the flexibility of railroad tracks for the dynamic analysis of vehicle-track interaction. In addition to being a complex structure, the flexible track is infinitely long and shows small areas of deformation whose position moves with time. Due to these properties, the efficient modeling of the track as a flexible body in a multibody system formalism is a challenging problem. In this work the model is developed using the moving modes method in combination with Krylov subspaces techniques. The moving modes method that was previously presented by the authors defines the deformation modes in a trajectory frame whose position changes with respect to the flexible track. In this paper the moving modes are selected from a detailed finite element model of the track and a model order reduction technique based on Krylov subspaces. These modes of deformation are adequate to be selected as moving modes since they affect a small area of the flexible body and they are obtained by assuming the load distribution that actually takes place during the dynamic interaction. However, the most interesting property of the Krylov subspace modes is that they can be selected such that the frequency response function of the reduced order model matches that of the full model with the desired degree of accuracy. In this paper a multibody formulation of railroad vehicles and flexible tracks based on the trajectory frame is presented and applied to the numerical simulation of a full railroad car on a track with geometric irregularities.