Dynamics Study Of Vibro-impact System With Nonlinear Spring-damper

Vibro-impact system is a common nonlinear dynamic system.The dynamic response of such systems become very complex because of the nonlinearity and singularity which is caused by the collision and impact. Its study has some theoretical difficulty. Gap-containing two degrees of freedom vibro-impact system can be seen everywhere in nature, science and social life. Collision of mechanical systems especially, causes failure, damage and shorten the life of equipment, not forgetting to mention the increase of noise level in the equipment. Therefore, there is an urgent need for a deeper and more comprehensive understanding of the dynamic nature of the vibro-impact system. The study of problems related to vibration and collision is of great significance to understanding the dynamics of a vibratory system and the impact vibration system so as to optimize the design, reliability and noise reduction of the system.The most critical problem of the collision is to describe the contact forces during collisions. Collision occurs, the structure of the collision objects make local deformation. There is stress wave propagation in the Collision objects. It is difficult to_describe the duration of the force change in the contact area and collision by a simple mathematical model.In this paper, the continuous contact model is used to explain local deformation in the collision and also to establish that in the process of collision there is a continuous collision force. The kind of vibrating system with nonlinear spring-damper model is based on Hertz contact force model. Such model can accurately reflect the deformation and energy loss of the colliding bodies, and compared to just simply using the restitution coefficient to describe the speed before and after the collision, the measurements of the above model are closer to reality. In this paper, the bifurcation diagram, phase diagram, the time-response graph, Poincare map diagram, Lyapunov exponent, fractal dimension map, the frequency spectrum and a combination of methods are used to study the dynamic behavior of the system. In this study, n=1and n=2corresponds to the different contact surface shapes. The collision law of motion and dynamic response of the system under different parameters were studied. The results of the study shows that the system dynamic response exhibits doubling bifurcation, Hopf bifurcation and pitchfork bifurcation, symmetric periodic motion, asymmetric periodic motion, opposing periodic motion and similar type of periodic motion and all these confirm a very complex nonlinear behavior is being exhibited. Analysis of the impact of different parameters on the dynamic response, provides some guidance and parameters for the design of systems wherein collision occur.This paper also studies the model based on the collision vibration system with dry friction. By means of calculation, we will be able to discover the laws governing the vibro-impact system with dry friction. From the bifurcation diagram we can clearly see some instability crises and viscous movement. Studied the influence of different parameters on the dynamic response, we find the parameters of the System μ1,μm, v have a major impact on the dynamic response of the system.