Communications in Mathematics 32 (2024), no. 1, 35–47 DOI: https://doi.org/10.46298/cm.10774 ©2024 Nouzha Lamdouar, Chakir Tajani and Mohammed Touati This is an open access article licensed under the CC BY-SA 4.0 35 Dynamic behavior of a railway track under a moving wheel load modelled as a sinusoidal pulse Nouzha Lamdouar, Chakir Tajani and Mohammed Touati Abstract. The aim of this paper is to evaluate the train/track induced loads on the substructure by modelling the wheel, at each instant, as a moving sinusoidal pulse applied in a very short period of time. This assumption has the advantage of being more realistic as it reduces the impact of time on the load definition. To that end, mass, stiffness, and dumping matrices of an elementary section of track will be determined. As a result, the equations of motion of a section of track subjected to a sinusoidal pulse and a rectangular pulse respectively is concluded. Two numerical methods of resolution of that equation, depending on the nature of the dumping matrix, will be presented. The computation results will be compared in order to conclude about the relevance of that load model. This approach is used in order to assess the nature and the value of the loads received by the substructure. 1 Introduction Various theoretical and experimental researches have been performed in order to assess train/track induced loads on the substructure. Mohammed Touati and al. [1] determined the loads induced by a non-linear 3D multi-body modelled train on the track with taking into account wheel/rail contact properties and track irregularities. Yang Xinwen and al. [2] MSC 2020: 74S05, 37M05, 74-10, 37N30 Keywords: Dynamic properties, Finite elements modelling, Railway track dynamics, Sinusoidal pulse load. Affiliation: Nouzha Lamdouar – Civil Department, Mohammadia School of Engineers, Mohammed V University, Morocco E-mail: nlamdouar@gmail.com Chakir Tajani – Department of Mathematics, Polydisciplinary Faculty of Larache, Abdelmalek Essaadi University, Morocco E-mail: chakir_tajani@hotmail.fr Mohammed Touati – Civil Department, Mohammadia School of Engineers, Mohammed V University, Morocco E-mail: mohammed.touati87@gmail.com arXiv:2301.01524v2 [math.NA] 12 Jan 2023