Double Sub-Resonance Mechanism in Torsional–Flexural Vibrations of a Double-Track Short Bridge Under a Moving Train

Abstract

Train-induced resonance of a railway bridge occurs when the train speed coincides with the primary resonance speed ([Formula: see text]) of the bridge, from which we can determine the sub-resonance speed as ([Formula: see text]). The primary resonance speed of a short bridge is generally much higher than the operation speeds of current high-speed trains but the corresponding sub-resonance speeds probably lie in the operation speed range. Such a resonance scenario can be observed from the vibration of a double-track bridge subjected to an eccentrically moving train, in which the deck vibration is combined by the vertical-flexural and torsional vibration modes of the bridge. Once the two modal sub-resonance speeds coincide with each other, a double sub-resonance will be developed on the bridge. In this study, an iteration-based train–bridge interaction finite element procedure will be presented to demonstrate the double resonance phenomenon. As expected, the double resonance may bring about a dramatic amplification on deck vibration. Such an excessive vibration is harmful to ballast stability and track maintenance of railway bridges.