19. Dynamic Analyses (Modal and Force Vibration) in a Railway Vehicle Model with 25 Degrees of Freedom

In this work, the modal and the forced vibration dynamic analyses are carried out in a railway vehicle model with 25 degrees of freedom. The objective of this work is to study the dynamic characteristics (modes and frequencies of vehicle vibration), as well as the analysis of forced vibration, allowing the simulation of resonance conditions and their critical speeds, important for the study of vehicle stability, safety, and passengers’ comfort. The tridimensional model has a passenger car body, two bogies, and four wheelsets. Models of vertical, lateral, and rotational track irregularities are used. In mechanical contact between wheels and rails, the theories of Hertz and Kalker, and also Vermeulen and Johnson are used. The equations of motion of the coupled system are numerically integrated using the Newmark Method, in the MatLab software. It is possible to conclude that the railway track irregularities associated with critical traffic speeds produce vibrations in the vehicle. Due to the damping of the system, these vibrations are attenuated between the rigid bodies through the primary suspensions, between the wheels and bogies; and secondary suspensions, between the bogies and the passenger car body.