Modal and Forced Vibration Analyses in a Railway Bridge considering Train-Track-Bridge Interaction

Abstract

This work investigates the dynamic response and modal behaviour of a railway bridge subjected to moving loads by considering complex train-track-bridge interaction (TTBI) models. The bridge structure, comprising simply supported concrete beams, is modelled using 3D Euler–Bernoulli finite elements with Rayleigh damping. The track integrates 3D rails with discrete spring-damper systems representing sleepers and ballast, incorporating vertical, lateral, and rotational irregularities via harmonic functions. Wheel-rail contact mechanics employ Hertz and Kalker theories alongside the Vermeulen and Johnson model for saturation and geometric non-linearities. The vehicle system consists of an 8-car train formation, with each unit modelled as a rigid body assembly featuring 25 degrees of freedom. Modal analysis successfully identified vertical bending, lateral bending, torsional, and longitudinal vibration modes. Forced vibration analysis under critical speed conditions demonstrated that envelope variations are governed by resonance phenomena and discrete loading cycles from sequential axle passages. Mid-span vertical accelerations complied with Eurocode EN 1990 A2 safety limits, while primary and secondary suspensions effectively attenuated vibrations. The findings demonstrate the critical role of TTBI modelling in evaluating structural safety and provide operational speed windows to preserve permanent way integrity during train passage.