An approach for modeling long flexible bodies with application to railroad dynamics

Considering track flexibility in railroad vehicle simulations can lead to improved results. In modeling a railroad vehicle as a multibody system, track flexibility can be incorporated by using the floating frame of reference formulation (FFRF), which describes rail deformations in terms of shape functions defined in the track body frame of reference. However, the FFRF method is subject to two serious shortcomings, namely: it uses unreal track boundary conditions to calculate shape functions and requires a large number of functions to describe deformation. These shortcomings can be circumvented by defining shape functions in the trajectory frame of reference. Based on this notion, a new form of FFRF that can be used to describe the dynamics of long bodies subjected to moving loads (cable cars, zip-lines, elevator guides, pantograph catenary mechanism, etc.) was developed here. The shape functions selected in this work are based on the steady deformation exhibited by a beam on a Winkler foundation under the action of a moving load. However, other sets of shape functions more appropriate for transient dynamics are suggested. The definition of the deformation shape functions in a frame that moves with respect to the flexible body produces new terms in the generalized inertia forces of the flexible track. The proposed approach was applied to an unsuspended wheelset traveling on a tangent track supported on an elastic foundation. The results thus obtained under variable foundation stiffness conditions are discussed and comparisons made with the case of a rigid track. The new approach is also compared with the moving mass problem as solved with the mode superposition method.