Stability of Beam Bridges Under Bridge-Vehicle Interaction

In this paper, we provide an accurate and reliable formulation for simulating the interactions of both train/bridge subsystems and suitable for high-speed railway lines as well as for existing lines worldwide that are being renewed or modernized. We model the train as a series of suspended masses, taking into account the energy dissipation and the suspension system for each train vehicle. On the other hand, the bridge supporting the rails with irregular elevations will be modeled as an Euler-Bernoulli beam. The mathematical formulation of the interaction problem between the two subsystems requires the writing of two sets of equations, which interact with each other through contact forces. Using a one-dimensional finite element formulation, a series of equations are constructed by Modeling the beam structure. In addition, the suspended mass equations are first discretized using Newmark's finite difference formulas, which then reduce the degrees of freedom (DOF) of the vehicle to those of the bridge element. This solves the coupling problem between the two subsystems. The derived component is known as the vehicle/bridge interaction (VBI) element. On the other hand, an iterative procedure will be used subsequently to solve the non-linearity problem of the resulting system of differential equations. MATLAB programs provide results that identify the critical parameters influencing the bridge's dynamic stability.