Non-Linear Analysis of The Dynamic Vertical Track-Bridge Interaction of a Simply Supported Skewed Railway Bridge

¹ Department of Physics, Mechanics and Civil Engineering Laboratory, Faculty of Sciences and Technology of Tangier, Abdelmalek Essaadi University, Morocco.
² Department STIC, STIC Laboratory, Team 3M, National School of Applied Sciences of Tetouan, Abdelmalek Essaadi University, Morocco

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 13 May 2026

Abstract

The objective of the present study is to investigate numerically the contribution of the vertical track to the vibratory response of a skewed girder bridge, incorporating single ballasted track, under the excitation of trains circulating at constant speed. Compared to a straight beam-type structure, the present model considers two types of ballasted track behavior: one nonlinear elastic, stiffening with the applied force, and the other linear elastic. This comparison also accounts for the structural skew of the structural deck, a geometric detail that is often overlooked. This approach aims to assess the extent to which incorporating such nonlinear effects of the interaction mechanism can alter the bridge’s behavior, particularly at resonance. The partial differential equations governing the vertical motion of the mechanical system are solved using two numerical methods to approximate the solution. The numerical results indicate that this type of nonlinearity in comparison to linear model cannot be neglected and its contribution is still moderate to the response of the mechanical system.