Research On Dynamics Of High-dimensional Vibro-impact System

High-dimensional constraint vibro-impact system is very common in mechanicalengineering field, and has great influence in mechanical equipment. It already attractedscience researchers domestic and overseas. Impact leads to strong nonlinearity anduncontinuity, general linear analysis is no longer applied to this kind of systems, thus newmethod is needed in analysis. This article made some specific researches in thehigh-dimensional constraint vibro-impact system. Researches on this article are as below:Firstly, it based on a single-degree-of-freedom vibro-impact system, establishing itsPoincaré map and analyzing dynamic behavior and bifurcation type of the system; parametricvariation can probably lead to essence variation of the system, doubling bifurcation and chaosbehavior occurs. Thereafter adding damping into dynamics in order to control bifurcation andchaos behavior, it can effectively control chaos behavior. Increase damping of the system, ithas remarkable result in reducing the resonance respond and shortening its vibrationattenuation time history of the system. This chapter is for the following high-dimensionalanalyses.Secondly, a three-degree-of-freedom system model and its Poincaré map are established,and the analytical solution of periodic motion and its linearization matrix of the system arededuced. From the location and amount of linearization matrix eigenvalues crossing the unitcircle, the system is theoretical analyzed under suitable parameters. Doubling bifurcation andtwo types of typical codimension two bifurcation, Hopf-Hopf bifurcation and Hopf-flipbifurcation of the system firstly take place. In doubling bifurcation, during the process fromdoubling bifurcation to chaos of the periodic motion in the system, there is quiet complicatedunconventional transition process and splendid dynamics behavior; the routes from torus burstand quais-periodic attractors of type “drop” to chaos are analyzed in Hopf-flip bifurcation; inthe first Hopf-flip bifurcation, flip bifurcation firstly takes place, then the Hopf bifurcation ofthe period two point occurs, two attracted invariant circles formed, finally transits into chaosvia phase lock; in the second Hopf-flip codimension two bifurcation, two kinds ofunconventional routes from torus doubling bifurcation and “shell” quais-periodic attractor tochaos are studied. It is revealed that there is complicated and abundant dynamics behaviornear codimensional two bifurcation of the high-dimensional vibro-impact system.At last, a dynamic model of the whole vehicle of passenger car is established, mainlydiscusses the snaking motion and bifurcation behavior in straightness pathway of it. Inmodeling, influence factor such as creep force, flange force and system suspension force areconsidered; thus the dynamics differential equation of the coach wheel set and its wholevehicle are established. Impact of passenger car system wheel track and stability of snakingmotion and bifurcation behavior under Poincaré map in maximum framework placement areanalyzed, during this analysis process, there are different kinds of dynamic behaviors in the system, such as symmetrically periodic motion, period-doubling bifurcation, Hopf bifurcation,quasi-periodic motion and chaos state of motion. Based on specific analyze of dynamicsbehaviors of passenger car system under Poincaré map, thus gives theoretical basis to theresearch on speeding up whole vehicle vibro-impact dynamics.