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

Y. J. Wang

School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, P. R. China

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J. D. Yau

https://orcid.org/0000-0002-9310-4575

Department of Architecture, Tamkang University, New Taipei City 251301, Taiwan

E-mail Address: jdyau@mail.tku.edu.tw

Corresponding author.

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J. Shi

School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, P. R. China

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, and

S. Urushadze

Institute of Theoretical and Applied Mechanics, Czech Academy of Sciences, Prague 19000, Czech Republic

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https://doi.org/10.1142/S0219455422710055Cited by:5 (Source: Crossref)

Abstract

Train-induced resonance of a railway bridge occurs when the train speed coincides with the primary resonance speed ( $v_{br}$ $v_{br}$ ) of the bridge, from which we can determine the sub-resonance speed as ( $v_{br} ∕ n |_{n = 2, 3}$ $v_{br} ∕ n |_{n = 2, 3}$ ). 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.

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