Analysis of resonance mechanism and conditions of train–bridge system

In this paper, the resonance mechanism and conditions of train–bridge system are investigated through theoretical derivations, numerical simulations and experimental data analyses. The resonant responses of the bridge induced by moving trains are classified into three types according to different resonance mechanisms: the first is related to the periodical actions of moving load series of the vertical weights, lateral centrifugal and wind forces of vehicles; the second is induced by the loading rate of moving load series of vehicles; the third is owing to the periodically loading of the swing forces of the train vehicles excited by track irregularities and wheel hunting movements. The vehicle resonance is induced by the periodical action of regular arrangement of bridge spans and their deflections. The resonant conditions are proposed and the corresponding resonant train speeds are determined. The application scopes of resonance conditions are discussed. The resonance of the train–bridge system is affected by the span, total length, lateral and vertical stiffness of the bridge, the compositions of the train, and the axle arrangements and natural frequencies of the vehicles. The resonant train speeds for some bridges are estimated and are compared with the critical train speeds obtained from the dynamic simulation of train–bridge interaction model or from the field measurements.