Train-Track-Bridge Interaction Analytical Model with Non-proportional Damping: Sensitivity Analysis and Experimental Validation

Recent studies related to the dynamic response of railway bridges focused on gradually increasing the model complexity of the train-bridge interaction, however, did not always discuss any experimental validation. In the present work, the authors analyse the role of the ballast in the dynamic train-track-bridge interaction (TTBI). The analytical response of Euler-Bernoulli (EB) beams is coupled with a distributed springs layer modelling the ballast. The two equations are solved with trainloads as elementary moving load excitation, avoiding too complex models. This non-classically damped problem has been solved with a Runge-Kutta finite-difference method with temporal-spatial discretization. Furthermore, the authors experimentally validated the mathematical TTBI solution, comparing it with the displacement response of a case study. Specifically, at first, experimental modal bending stiffness parameters have been estimated to provide a representative equivalent EB beam model. Thereafter, the coupling effects of the ballast have been considered with a sensitivity analysis of the modelling parameters. Finally, the optimization to the actual experimental response of the model provided an estimate of the vertical ballast stiffness and its damping. The relevant difference in the damping of the experimental and mathematical model evidences the fundamental role of the ballast in adsorbing vibrations induced by the train passages.