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This study examines the effect of vehicle–bridge interaction (VBI) on the vibration of coupled train–bridge systems and proposes a consistent approach to decouple the VBI problem; the Extended Modified Bridge System (EMBS) method. This constitutes an extension of the formerly developed, for simply supported bridges, Modified Bridge System method. The analysis considers a generic, multi-degree of freedom (MDOF) vehicle–MDOF bridge configuration, representative of a wide class of practical train–bridge systems. This approach enables the MDOF representation of the constituent VBI mechanisms on the mechanical system of the bridge. Based on an asymptotic expansion analysis of the coupled system response, the study brings forward the dominant coupling parameters and their relative importance on the bridge response. The proposed decoupling EMBS method solves the bridge independently of the vehicle by changing its mechanical system via additional damping, stiffness and loading terms. The MDOF description of these terms makes the proposed scheme appropriate for involved bridge configurations, such as continuous and arch bridges. In addition, it allows the accurate estimation of the deck acceleration of bridges, which is an important serviceability limit state. Numerical examples demonstrate the accuracy and efficiency of the EMBS method compared with the solution of the fully coupled system and other decoupling methodologies. Lastly, the proposed approach is simpler than the coupled analysis, which can be of particular importance in bridge design practice.

MDOF extension of the Modified Bridge System method for vehicle–bridge interaction