Analysis of Train-Track-Bridge Interaction using Modal Superposition and Moving Track Method

초록

The analysis of Train/Track/Bridge interaction has been done in depth for a long time, in vertical direction(2D) only or including lateral direction(3D). However almost every trial to analyze the interaction among them simplifies some of each components because the 3D interaction analysis needs huge amount of time for calculating train/track/bridge behaviours. The modal superposition is a good alternative to reduce such amount of calculations remarkably, in a sense that the total degrees-of-freedom(D.O.F.s) of bridge can be expressed as a few mode shapes and their natural frequencies. Even the use of modal superposition technique cannot be efficient for the case of long-span bridges because the track length gets longer and the D.O.F.s of track itself are still large. And the time step could be divided into a few micro seconds in order to calculate the detailed wheel-rail contact force in consideration of rail movement which is induced by moving train on the long-span bridge. Therefore an efficient method to analyze the interaction of train/track/bridge is necessary. This paper proposes a method which models the short-length track which can move according to the running train, and can be connected to the bridge by modal superposition. Some assumptions and basic equations are derived to express the moving track and system matrix which uses the direct stiffness method and modal superposition method in a way. The proposed method can efficiently reduce the total D.O.F.s under consideration and finally the CPU time needed. It produces good agreement with the result of the full track model and is estimated to be used easily in evaluating the running safety and riding comfort of train on the long-span bridges."