Simplified Analysis of The Dynamic Longitudinal Track-Bridge Interaction of a Simply Supported Railway Bridges

In the present work, the core idea is to analyse the influence of longitudinal track-bridge interaction (TBI) on the vibratory response of a simply supported (S-S), single-track, skewed bridge beam crossed by moving high-speed trains. The bridge is modeled as a uniform Bernoulli-Euler (B-E) composite beam with two layers connected continuously by horizontal spring and dashpot elements at the slip interface. The skew angle effect is incoporated – refering to a prior model - iuat both ends of the beam using two rotational spring elements, ensuring that the bridge’s behavior is governed sololy by bending modes. By considering the fundamental mode of vibration, two numerical schemes – the Runge-Kutta method (RKM) and the Finite Difference Method (FDM) – are employed to validate the simulation results. The obtained results demonstrate that the system is shown to exhibit dynamic behavior governing by a Duffing-like oscillator. Furthermore, they reveal that even the presence of the bridge’s skew angle, the ballast introduces additional stifness and damping. These effects generally to increase the fundamental frequency, in consequence raising the critical speed, while reducing the response amplitude both at resonance and non-resonance situations.