Research On Bifurcation And Chaos Of Complex Nonlinear Vibration System

Nonlinear vibration is a common phenomenon in engineering practice, such as vibratory shakeout machine, vibratory roller and piling machine used in the production of society, which all utilize collision between parts or objects principle to achieve the desired results and objectives of the work; however, in the mechanical production process, the existence of boundary or internal clearance leads to the collision between the parts, which have an adverse effect on dynamic load and production efficiency of the mechanical system. Therefore, the research and control of the nonlinear impact vibration system in our life has very important theoretical significance and practical value. In this paper, three mechanical models is simplified and established based on the mechanical equipment in production practice, and studied the dynamic characteristics of each model under the condition of parameter.Firstly, the concept of chaos is described. The bifurcation definition, Poincaré map and Floquet theory of nonlinear vibration is introduced simply. Then the paper sets out the developing process and research method in recent years of nonlinear dynamics in detail. Aiming at the problem of collision vibration system, the structure and content of the paper are established.Secondly, the pile driver is taken as engineering background, the chaos and bifurcation of two-degree-of-freedom of the unilateral rigid vibro-impact system is studied. According to the theoretical derivation, the periodic solution, Poincaré map and Linearization matrix of the system are solved. It is confirmed that the system not only exist period-doubling bifurcation, Neimark-Sacker bifurcation, but also has Hopf Bifurcation and the results show that the phase graph and the time-history graph are periodic changed through the method of numerical simulation. Finally, the dynamical behavior and the way to chaos of the system is found with the variation of dimensionless parameters.Thirdly, the paper described a three-degree-of-freedom of the rigid vibro-impact system about impact damper. The analytical solution of periodic motion is deduced and the Floquet theory is used to analyse one situation of linear matrix eigenvalues which cross the unit round. It can be find that the invariant circles on Poincaré section can express Quasi periodic motion and the different types of bifurcation occurs respectively in the entire range of system parameter variations ??? ?_c1 and the different paths of chaos through computer numerical simulation. The control parameter is very important to the bifurcation and chaos of a system, and it can change the motion process of the whole system.Fourthly, the hook collision of coupler and draft gear in engineering practice as the research background, a mechanics models of four-degree-of-freedom of the rigid vibro-impact system is set up. Based on the numerical simulation of the dynamic characteristic, the bifurcation and the chaotic state under different parameters are studied. With the change of control parameters, the period-doubling bifurcation, Hopf bifurcation, Hopf-flip codimension two bifurcation and torus doubling bifurcation are occurred in the system, finding out that the sensitivity of the high dimension vibro-impact system is comparatively large by comparing with the low dimension system. Therefore, parameter selection and control have a great effect on the optimization of the high dimension vibro-impact system.