Application of the trajectory coordinate system and the moving modes method approach to railroad dynamics using Krylov subspaces

This paper presents a procedure that makes use of a particular formulation based on the trajectory coordinate system (TCS) approach, which is specific of ground vehicles, to describe the track deformation by means of a suitable set of mode shapes. The inertia terms of the track elastic displacements are derived using the TCS arc length to couple the system dynamics. The selection of the track modes of deformation is carried out from a finite element model by using Krylov subspaces as the model-order reduction technique. The modes of deformation move along the track fixed to the TCS using the moving modes method (MMM), avoiding the issue concerning the spatial convergence of the load (wheels) on the track and preserving their vertical frequency contents whose accuracy can be chosen beforehand. An unsuspended wheelset with an induced hunting motion moving on flexible and rigid tangent tracks and a vehicle model are simulated using rail defects as excitations sources such that the performance of this procedure using a fully 3D contact algorithm is shown and analyzed.