Keywords: bridge-train dynamics, bridge-train interaction, dynamic response, finite element analysis, dynamic testing, experimental verification.

The paper summarises a part of the study on the dynamic response of railway bridges subjected to moving trains. The primary objectives of this study were threefold: firstly, to develop an accurate and computationally efficient three-dimensional numerical model for bridge-train dynamics; secondly, to extensively verify this model; thirdly, to investigate the dynamic response of bridge-train systems and the bridge-train interaction. This paper covers the first two objectives. The study was partly driven by an industry need for extended methods of analysis and enhanced modelling capabilities to handle bridge-train dynamics problems. This research also aimed to enhance the knowledge on dynamic response of existing railway bridges. Developments in the modelling capabilities and in the understanding of the dynamic response of bridge-train systems could provide refined methods of analysis and assessment of existing structures. These, in turn, would help to address a problem of ageing bridge stock and allow for more cost-efficient methods of dealing with dynamically deficient bridges. Enhancements to the capacity of railway networks and travel times can also be effected if dynamic effects resulting from increased speed and load of trains are accurately predicted and assessed.

The literature review carried out in preparation to this work identified limitations in modelling capabilities for bridge-train dynamics [1]. In order to partly address these limitations a numerical model with three-dimensional capabilities, entitled DBTI, was developed. Within DBTI, bridges are modelled with beam-type finite elements that were derived using linear Lagrange's and cubic Hermite's shape functions by applying the displacement-based method. Trains are represented by sets of multi-body vehicle models with a generic model of a six-axle railway vehicle with dual-stage suspension that was derived utilising d'Alembert's principle and the direct-stiffness method. This model allows for three-dimensional representing of six axle railway vehicles, a feature that, to the authors' knowledge, has not been previously documented in studies on bridge-train dynamics. The solution procedure utilises direct integration Newmark's method combined with a modified Newton-Raphson iteration and relaxation technique for improved convergence of the solution.

In order to provide a solid base for further developments and studies, the model was extensively verified, both theoretically and experimentally. Theoretical verification involved comparison of the results produced by the DBTI package with other well-established methods of solution of bridge-train dynamic problems. Experimental verification, that was found to be rarely attempted by other researchers, included modal tests and dynamic response tests. The former were carried out to identify dynamic parameters and calibrate the finite element model of the bridge, whereas the latter recorded the response of the bridge to moving trains and allowed for direct comparison with DBTI's displacement and acceleration responses. Both verification procedures ensured good accuracy and reliability of the DBTI package.

1

Majka, M., "Dynamic response of railway bridges: Analysis of bridge-train interaction using numerical and experimental techniques", PhD Thesis, Department of Civil Engineering, National University of Ireland, Galway, Ireland, 2006.

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