Nonlinear Vibration And Bifurcation Of Asymmetric Piecewise Systems

In this paper, in order to study the vertical dynamics of heavy trains bogies, boththe average method and singularity theory are used to discuss the effects of load andexcitation amplitude on the nonlinear vibration and bifurcation behaviors, andmeanwhile the axle elastisity dry friction and other factors are ignored. The vibrationof system is researched by getting the different kinds of amplitude frequency responsecurve, The study may provide guidance for the design and improvement of bogies.This article consists of five parts:Part I, introducing the development of nonlinear dynamics, the background ofpiecewise linear system, and the definition of bifurcation theory. Describing thestructure and development of trains bogies.Part II, the single degree of freedom model involving asymmetric piecewiseforces is established for the vertical dynamics of heavy haul freight trains bogie. Dueto the changes of load, the model is expressed in different forms for the two casesunder light and heavy load respectively.Part III, the amplitude frequency response equations are derived for both cases byusing the average method. Then by using the singularity theory for constrainedbifurcations, the effects of the load and the excitation amplitude are analysedthroughtly and fourteen types of qualitatively different amplitude frequency responsesare obtained.Part IV, in order to verify the theoretical results, the responses are calculatednumerically and displayed in different diagrams including time history, phase plane,Poincare map. Meanwhile the Poincare bifurcation diagram is used to adopted tostudy the effects of the load variation. Getting the amplitude frequency response curve,and contrasting the numerical results with the theoretical results. The numericalresults show that the analytical results have high precision for small excitationamplitudes.Part V, summary of the thesis.