Dynamics Research On Multi-degree-of-freedom Nonlinear Vibration System

In engineering practice, on the one hand, we should effectively relieve the deformationand destruction, it not only need shockproof on the transportation such as cars, trains andplanes, but also apply in bridge and nuclear power plant engineering structure; on the otherhand, we need to make full use of the feature of vibro-impact, and work out various kinds ofinstrument and equipment that based on vibro-impact theory, such as lithoclast, pilehammer, punch.This article gives brief introduction to multi-degree-of-freedom nonlinear vibro-impactsystem, first discusses the latest research direction and conclusion on bifurcation and chaosproblem of the power machinery which developing by scholars domestic and overseas, thenstudies their method for vibrate properties of researching nonlinear system. This articleincludes three chapters:1. First, a single-degree-of-freedom vibro-impact system is studied, physical modeland its motion differential equation are established, chaos phenomenon is shown up, thechaos phenomenon and the routes to chaos are analyzed.2. Secondly, the physical model and its differential equation of athree-degree-of-freedom vibro-impact system are established; the mathematics expressionform of differential equation periodic solution is got from analytical solution. Then solvingby programming with MATLAB, complicated dynamics behaviors like periodic motion ofvibro-impact system, Hopf-filp codimension two bifurcation, Hopf-pitchfork codimensiontwo bifurcation and the routes to chaos are studied. Complicated dynamics behaviors nearcodimension two bifurcation point of the high-dimensional vibro-impact system are shown.3. At last, a dynamics model of six-axis locomotive bogie system is established, thecreep rate and creep force between wheel track, at the same time the condition of wheel setand framework is analyzed. Taking advantage of the theory deduced by motionaldifferential equation of the multi-degree-of-freedom system, and work out the motionaldifferential equation of different parts in passenger car bogie system of car combiningNewton’s second law. Thus the visual numerical results like global bifurcation, phasediagram, Poincaré map, and response diagram of the system are worked out. Influencefactor such as creep force, flange force and system suspension force are considered, adynamic model of a six-axis locomotive bogie system is established, the dynamicsdifferential equation of locomotive wheel set and its framework is solved. The wheel trackcollision between six-axis locomotive bogie system and snaking motion and bifurcation behavior under Poincaré map are analyzed, find out that there are variety of dynamicsbehaviors, such symmetrically periodic motion, period-doubling bifurcation, reversedperiod-doubling bifurcation and chaos state of motion. Dynamic behavior of locomotivebogie system under Poincaré section is analyzed specifically, and it offers theoretical basisfor research on impact dynamics of speeded up locomotive wheel track.Conducting dynamics analysis with a model in engineering practice, and makingfurther analysis for the results, then choosing proper system parameters, controlling badchaotic phenomenon, optimization design then improve existing mechanical system. Itshows application value of chaos in engineer practical.