Resonance of high-speed trains moving over a series of simple or continuous beams with non-ballasted tracks

For a train composed of a number of identical cars moving over a bridge at high speeds, train-induced resonance on the bridge may occur when any of the frequencies of the bridge coincides with any of those implied by the wheel loads. On the other hand, for a vehicle moving over a series of bridges with identical spans at constant speeds, bridge-induced resonance on the vehicle may occur when any of the frequencies of the vehicle coincides with any of those of the bridges. The objective of this paper is to provide a complete coverage for the train-induced and bridge-induced resonances on the train-bridge system using both the analytical and finite element approaches. Focus will be placed on the interacting resonant mechanism between the two subsystems of the moving train and the bridge. In addition, a vehicle-bridge interaction (VBI) element considering the rails effect is developed. The numerical examples indicate that the train-induced resonance on the bridges takes place at higher speeds, but the bridge-induced resonance on the train cars at lower speeds. Neglecting the rails effect may underestimate slightly the beam response in the high-speed range, and less slightly the moving vehicle response for all speeds considered.