The interaction between the train, track, and bridge was considered as an interaction between two decoupled subsystems. A first subsystem consisted of the train vehicle simulated as a four-wheelset mass-spring-damper system having two layers of suspensions and ten degrees of freedom. A second subsystem consisted of the track-bridge system assumed to be a top rail beam and a bottom bridge beam coupled by continuous springs and dampers representing the elastic properties of the trackbed smeared over the spacing of the railway ties. The bridge supports were assumed to be rigid or flexible. The equations of motion of a finite element form were derived for each subsystem independently by means of the Newton’s second law. The dynamic interaction between the moving vehicle of the first subsystem and the stationary underlying track-bridge structure of the second subsystem was established by means of a no-separation constraint equation in the contact points between the wheels and the rails. The proposed two-dimensional analysis was intended to accurately describe the vertical behavior of short span bridges subjected to high-frequency excitations due to the passage of high speed trains; therefore, shear deformations, rotational inertia effects, and consistent mass matrices were adopted in the mathematical model. Numerical solutions of the decoupled equations of motion for both subsystems were obtained with the step-by-step direct integration in the time domain using HHT alpha method with a special scheme in the contact interface. The solution accuracy of the proposed method was validated against responses obtained from a semi-analytical method of a train car travelling over a simply supported bridge. The practical engineering application was demonstrated with a case study investigating effects of key parameters in the behavior of a ballasted short span railway bridge. Compared with the moving force model, results showed that for bridges with rigid supports both the vehicle interaction and trackbed produce lower peak responses at resonance speeds with the latter being more significant. However an increase in support flexibility had a greater impact across all speeds in increasing the bridge responses.
High Speed Rail Short Bridge-Track-Train Interaction Based on the Decoupled Equations of Motion in the Finite Element Domain
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Nour, SI, & Issa, MA. "High Speed Rail Short Bridge-Track-Train Interaction Based on the Decoupled Equations of Motion in the Finite Element Domain." Proceedings of the 2016 Joint Rail Conference. 2016 Joint Rail Conference. Columbia, South Carolina, USA. April 12–15, 2016. V001T10A004. ASME. https://doi.org/10.1115/JRC2016-5785
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