Beta 1


Title Nonlinear railway vehicle dynamics
Author Gilles, Brieuc
Supervisor True, Hans (Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
Institution Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
Thesis level Master's thesis
Year 2004
Abstract We investigate the motion of a railway vehicle travelling along a straight track, with constant rolling velocity v. The model contains dry-friction dampers which introduce a stick/slip effect. We consider only three degrees of freedom, so that the impact of the stick/slip phenomenon can be more clearly detected. The dynamics are described by a nonlinear system of equations obtained by applying classical mechanics laws. The behaviour of the solutions turns out to be highly sensitive to the parameter v, as a complex sequence of bifurcations occurs all across the velocity spectrum 5m/s v 40m/s. Several different types of attractors are found - some are periodic, others are chaotic. We discuss two methods to estimate the largest Lyapunov exponent y1. The standard method involving Gram- Schmidt orthonormalizations is found to contain large but systematic errors. We therefore present a simple method for estimating these errors, and use the error estimates as correction terms. The resulting estimates of y1 are used to test for chaotic solutions across the velocity spectrum.
Imprint Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU : DK-2800 Kgs. Lyngby, Denmark
Keywords Nonlinear dynamics; chaos; Lyapunov exponents; bifurcations; railway dynamics; dry-friction; stick/slip.
Admin Creation date: 2006-06-22    Update date: 2012-12-21    Source: dtu    ID: 154753    Original MXD