Please cite this article as: Zboinski, K., Dusza, M. Self-exciting vibrations and Hopf's bifurcation in nonlinear stability analysis of rail vehicles in a curved track, European Journal of Mechanics / A Solids (2009), doi: 10.1016/j.euromechsol.2009.10.001 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Abstract -the main objective of this article is to present the authors' view of-and results on non-linear lateral stability of rail vehicles in a curved track. Three elements are exploited in order to secure this objective. Firstly, physical genesis of the problem is discussed, and its similarity to straight track analysis is emphasized. Results of the theories of self-exciting vibrations and bifurcation are the key elements here. Secondly, the method suitable for analysis in a curved track is presented. New necessary elements, extending the better established methods for straight track are clearly mentioned and described. The methodology of building original stability maps, being the basis for the analysis and valid for whole range of curve radii and straight track is represented. Thirdly, a sample of the analysis is shown in order to give the idea how the method can be utilised. The case study refers to the influence of wheel/rail profiles on the stability in circularly curved track and straight track as well. Two different pairs of wheel/rail profiles are used and the corresponding results compared. The main contributions of the article are: a discussion of the physical nature of phenomena related to the stability in a curved tracks, and the method (procedure) established for the reasons of the analysis. Another and more general contribution is our say in the hot polemics on the advisability of stability analysis in curves and the advantages of the non-linear critical speed over the linear one. M A N U S C R I P T A C C E P T E D ARTICLE IN PRESS Self-exciting vibrations and Hopf's bifurcation in non-linear stability analysis of rail vehicles in a curved track

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The article presents authors' recent results on nonlinear lateral stability of rail vehicles in a curved track. The theories of self-exciting vibrations and bifurcation are the key elements here. The general objective is presentation of extended use of the earlier worked out authors' method to more complex rail vehicle models. Two 4-axle vehicle models were created. The first one represents coach MKIII described with multibody software by the first author. The second one represents coach 127A described with use of engineering multibody software VI-Rail. The models are described, and method of the analysis is shortly reminded. Then, results for both models are presented. They include verification of the limit cycle possible passage from straight track to circular curve and stability maps for regular curves of different radii and straight track. Next influence of selected suspension parameter and wheelrail coefficient of friction on vehicle stability is shown. The more general objective is the authors' say in the hot polemics on the advisability of rail vehicle stability analysis in curves and on the advantages of the nonlinear methods of such analysis over the linear ones.

Analysis of lateral stability of rail vehicle model is the subject of present paper. The method used by the author is based on bifurcation diagrams creation and analysis. The continued study of stability of vehicle model in straight track and curved track and form of the results presentation are original features of the method. Results for the straight track and wide range of radii of the curved track are presented jointly on the combined bifurcation diagrams in this paper. Multibody dynamics software VI-Rail was used for numerical analysis. Passenger vehicle model and track models were created. Analysis of track gauge influence on vehicle model stability is main aim of this paper. But analysis of possibility to adopt the method worked out earlier to the newly used numerical code and model of 4-axle vehicle is the aim either.