Abstract
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.
Highlights
The dynamic behavior of coupled vehicle–bridge systems is a topic of increasing interest
The present study extends the previous work of the authors [21,26], to the case of multi-degree of freedom (MDOF) vehicle–MDOF bridge systems, representative of practical train– bridge systems
Different to most decoupling methods, which are mainly tailored to particular bridge types, e.g., supported bridges [14,26], the proposed Extended Modified Bridge System (EMBS) approach is applicable to a variety of MDOF vehicle–MDOF bridge configurations
Summary
The dynamic behavior of coupled vehicle–bridge systems is a topic of increasing interest. Eurocode proposes combining the moving load approximation with a damping ratio, in addition to the structural damping of the bridge, to account for the favorable damping effect of VBI [20,24,25,26] This additional damping method (ADM) [14] applies to supported bridges and recommends an additional damping ratio [14] that is merely a function of the bridge’s length. Later studies [24,25,26] showed that the ADM does not accurately estimate the additional damping effect of VBI on a bridge, as this depends on the dynamic characteristics of both vehicle and bridge. Different to the formerly presented MBS method [21], the consideration of MDOF vehicle and MDOF bridge models enables the accurate prediction of the bridge deck acceleration
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