Analysis Of Double Degree Of Dreedom Vibration System With Chattering And Grazing

The chattering of collision vibration system with grazing phenomenon is a common phenomenon of nonlinear dynamics. In real life, collision vibration phenomenon around us every moment of the day, the study of it has been applied in machinery, physics, engineering mechanics, and even has been conducted in the field of applied mathematics. With the deepening of the research, experts, scholars found that the chattering phenomenon, use it to explain the accident caused a lot of reality, also explains the chatter phenomenon is likely to bring disastrous damage to people, so, the research on it become urgent. Also in the process of research, however, found another kind of phenomenon, glancing, it makes us study the Poincare mapping of collision vibration system produced a singularity, thus there are many complex dynamic behavior, so the research on the phenomenon of grazing and become very necessary, to prove the effect of.Collision in this paper, two classes of double degree of freedom vibration system is completely chattering phenomenon first made a theoretical analysis and deduction, analysis and calculation the chattering completion point is obtained and the chattering from beginning to end of time, secondly, through the C language programming the variable step fourth order Runge-kutta method is used for numerical simulation. From the global bifurcation diagram observations on vibration of the system the scope of the required parameters, and then, through the time response diagram observation system of chattering phenomenon, and observations of fully chattering time experienced by comparing with calculated theoretical derivation of the time.This article also collision of two classes of double degree of freedom vibration system of the grazing phenomenon is studied, using numerical simulation gives the first system along with the vibration frequency ω change of the global bifurcation diagram, the analysis of the global bifurcation diagram in the process of discovery system in the process of changing with excitation frequency ω appeared discontinuous bifurcation phenomenon, as a result, the preliminary judged caused by glancing collision. Secondly, through the numerical simulation system is given in the discontinuous bifurcation diagram, through the phase diagram clearly showed that the discontinuous bifurcation to wipe a phenomenon caused by.Collision of two classes of double degree of freedom vibration system of chattering and grazing analysis, found the system of the chatter phenomenon is divided into totally chattering phenomenon and the chattering phenomenon completely. Their difference is that a completely chattering phenomenon at the end of the chattering is there will be a state of adhesion, rather than completely chattering has no end of this stage directly. In the grazing phenomenon in the process of analysis, found the grazing phenomenon indeed led to the collision vibration system of Poincare mapping becomes discontinuous, make its produce singularity, led to the collision vibration system cycle number did not change, but adds a collision.