Research On Dynamics Of Multiple-degree-of-freedom In Vibro-impact System

In recent years, domestic and overseas expert have been made great progress in the research on Hopf bifurcation problems of periodic motion in one-degree-of-freedom or unilateral rigid constraints two-degree-of-freedom vibro-impact system, moreover, the multiple-degree-of-freedom in vibro-impact system which have fairly complex system parameter, many and misellaneous with trifles dynamic responses, sensitive for the effect of parameter on the stability of the system is seldom studied, numerical analysis is the main research method. Nevertheless, vibro-impact often exists on engineering practice in machinery, vehicles and so on. It is urgent to have a more comprehensive understanding for such dynamic behavior in the system.For this reason, in engineering practice, it is of great significance on the research for multiple freedom of the vibration system with clearance. Thus this article has been made comprehensive analyses for two-degree-of-freedom vibro-impact system and four-degree-of-freedom vibro-impact system. This article is mainly about:1. This article has been made comprehensive analyses on the dynamic behavior on two kinds of typical two-degree-of-freedom vibro-impact system and kind of four-degrees-of-freedom. By establishing physical model and mathematical model of the vibro-impact system, using regular modal matrix method to decouple the vibro-impact system, and working out the analytical solution, linear matrix and poincare mapping of different system by analytic method.2. Use Poincare map theory to analysis the fixed point instability and bifurcation for planar mapping analysis. When a certain eigenvalue of linear matrix is1or-1, there will be saddle node or doubling bifurcation; when there is double eigenvalues across the unit circle in linear matrix, codimension two local bifurcation phenomena will be in the system. Chose the appropriate system parameters, combined with tendency chart of linear matrix eigenvalues which cross the unit round, analysis the linear matrix eigenvalues under this situation, and study the dynamic behaviors like bifurcation and chaos evolution in the system.3. Aiming at specific physical model of multiple-degree-of-freedom vibro-impact system, under which parameter that the Hopf bifurcation and complex dynamic behavior of chaos occur is studied, the Poincare section graph of the system after the quasi-periodic motion, the periodic motion and the torus doubling to the chaos is shown.4. Making use of the result of numerical simulation, the effect of the key controls parameter on the periodic motion of the system is analysed, finding out that the sensitivity of the high dimension vibro-impact system is comparatively large, consequently, select the optimal parameters of the system is necessary for the optimization design in mechanical vibro-impact system.