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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