Selected Methods for the Investigation of Linear, Continuous and Discrete-Continuous Mechanical Models of a Rail

摘要

Dynamics of mechanical vehicle track systems are considered paying attention tothe models of a vehicle and track as discrete, continuous and discrete continuous systems. Methods of investigating these models are presented. Dynamic properties of simple linear discrete systems are considered and methods to compare dynamic properties of continuous and discrete systems are presented. For this reason the continuous track structure is assumed as a Bernoulli-Euler beam on Winkler foundation. Analytical solutions for continuous track models are presented. The track is modeled as a Bernoulli-Euler beam or a Timoshenko beam on Winkler foundation loaded with a harmonically oscillating force moving at a constant speed. Selected methods to investigate continuous and discrete continuous systems are presented. As mathematical models, the Fourier method of separation of variables applied to continuous finite systems and the Fourier integral method applied to a case of continuous infinite systems are used.