Movable FEM nodes in the problem of interaction between a moving mass and a prestressed beam

The study of beam vibrations under the influence of a moving locomotive requires the use of advanced mathematical methods. This paper focuses on the application of moving nodes in the finite element method (FEM). The Newmark method used in this work allows for high accuracy and stability of the numerical solution. Real conditions of beam support are taken into account using eccentricities. The calculation scheme takes into account the interaction of the beam with the supporting parts by modelling fixed and moving joints. This allows the mathematical model to closely approximate the description of dynamic processes. As the horizontal speed increases, the amplitude of vertical vibrations increases, which leads to an increase in the dynamic coefficient.