Resonance of a Series of Train Cars Traveling Over Multi-Span Continuous Beams

Abstract

For a train car moving over a multi-span continuous beam of identical span length L at constant speed v, it may encounter repetitive excitations transmitted from the sustaining beam of frequency v∕L excited by the previous passing cars. If the exciting frequency v∕L coincides with the vehicle frequency f c , namely v∕L = f c , resonance will be developed on the running car. In such a case, when the train car travels over more and more spans of the beam, the response of the car will be accumulated and becomes larger and larger, up to the limit imposed by inherent damping. Using the rigid-vehicle/bridge interaction finite element developed previously by the authors, each train car is modeled as a two-axle vehicle and each span of the continuous beam is simulated as a number of beam elements. Then the resonant response of the train cars running over the multi-span continuous beam is analyzed. The numerical examples indicate that for a high speed train composed of a series of cars traveling over a multi-span continuous beam, the train-induced resonance on the bridge takes place at a rather high speed, but the bridge-induced resonance on the train cars takes place at a much lower speed.