Analysis Of Nonlinear Dynamics In Impact Vibration System

In the paper, namely two two-degree-of-freedom vibro-impact system model and athree-degree-of-freedom vibro-impact system model as an object of study are specificallyanalyzed, Systematically describing bifurcation and chaotic dynamics phenomena that appearin the process of collision movement of these vibration systems. Derivation and analysis showthat,collision vibration dynamics behavioral characteristics are very different under differentdegrees of freedom, and the different constraints attachments conditions will cause differentdynamics behavior.In the first chapter, the concept of nonlinear vibration is described,and a brief descriptionof what is bifurcations and chaotic phenomena, as well as stability in the presence of periodicmotion appears chaotic system, listed in recent years for the study of non-linear movement inrealityapplications and research results in the corresponding engineering background, brieflyexplaining the main problems, while outlooking development direction of the future dynamicsof of nonlinear systems.The second chapter ivesrigid constrain the mechanical model of the two-degree-of-freedomvibration system, the movement and behavior of this model are analyzed, then make use of anumerical analysis method,theoretically deducing the periodic motion of the system.Regularmodal matrix is decoupled and the boundary conditions of the system is analyzed, and thusderive the analytic solution of the system and the Poincaré map, Finally, find out thebifurcation phenomena and the road to chaos of the system by the numerical programming,while these phenomena are analyzed.The third chapter gives a two-degree-of-freedom symmetrical collision dynamics model.Analyzing the periodic motion of the system and deducing the motion of the system accordingto the theory of numerical analysis, and the boundary conditions of the periodic motion ofsystem is analyzed, the analytical solution and the Poincaré map of the system are calculated.Finally, the chaper draws and analyzes the law of the process leading to the bifurcation andchaos as well as their evolution.The fourth chapter gives a three-degree-of-freedom vibro-impact model. The first themotion of the system are analyzed and decuded, then analyzing the boundary conditions ofthe system to draw analytical solution, and determining the Poincaré map of the system,Finally, the conditions and the behavior of the system leading to chaos are analyzed.