||Nonlinear railway vehicle dynamics
||True, Hans (Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark)
||Technical University of Denmark, DTU, DK-2800 Kgs. Lyngby, Denmark
||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.
||Department of Informatics and Mathematical Modeling, Technical University of Denmark, DTU : DK-2800 Kgs. Lyngby, Denmark
||Nonlinear dynamics; chaos; Lyapunov exponents; bifurcations; railway dynamics; dry-friction; stick/slip.
Creation date: 2006-06-22
Update date: 2012-12-21