Nonlinear railway vehicle dynamics | Brieuc Gilles
| | 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. | | Keywords | Nonlinear dynamics, chaos, Lyapunov exponents, bifurcations, railway dynamics, dry-friction, stick/slip. | | Type | Master's thesis [Academic thesis] | | Year | 2004 | | Publisher | Informatics and Mathematical Modelling, Technical University of Denmark, DTU | | Address | Richard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby | | Series | IMM-Thesis-2004-41 | | Note | Supervised by Assoc. Prof. Hans True | | Electronic version(s) | [ps.gz] | | BibTeX data | [bibtex] | | IMM Group(s) | Mathematical Physics |
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