Research On Sticking Motion And Grazing Bifurcation In Multi-Degree-of-Freedom Vibro-Impact Systems

Collision and vibration are very common phenomena in the mechanical system and the research is very important. One side, people use the basic principle of vibro-impact to design and manufacture a range of machinery and on the other side, the collision and the vibration cause the surrounding environment and mechanical systems many harmful effects. Only fully understanding of the basic principle of vibro-impact, we can better use it and prevent unnecessary loss. In this paper, a class of multi-degree-of-freedom system with more complicated constraint condition is considered.In the second chapter, through the basic method of study vibration, the vibration equations of multi-degree-of-freedom system are built. Then some basic concepts are introduced, such as natural frequency, principal mode, regular vibration model and so on. Finally through the vibration model transformation, we decouple the differential equations into the single-degree-of-freedom system, and use superposition principle to obtain the solutions of the free vibration equations.In the third chapter, we suppose that each degree of freedom is limited by a restriction of displacement. By the assumption of Rayleigh type ratio damping, taking dimensionless parameter and decoupling transform, the displacement-time response of the forced vibration system is solved. At the time of impact, we analysis the instantaneous impact model of the collision and find that when the impact happens, the smoothness of system is broken.Through numerical calculation, the fixed point of poincare mapping is found and the different impact type is determined.In the fourth chapter, a class of two degree of freedom system which may present periodic sticking movement is considered. Firstly, the conditions of the sticking movement are given, then a kind of two degree of freedom system are analyzed in detail. The results show that the system may have all kinds of the analytical solution of the sticking situation. Through the necessary condition for sticking motions, we prove that the two oscillators do not appear sticking when the constraints are in the different side at the same time. However when the constraints are located in the same side, the sticking motion may occur at the same time by adjusting the parameters. This case is called temporarily "motionless" situation. Finally, the numerical calculation verifies that the cycle sticking motion, rising phenomena and temporarily "motionless" situation exist.In the fifth chapter, by the conditions of the existence of periodic solution, a class of two degree of freedom system which may possess grazing periodic motion is considered.