Analysis On Nonlinear Dynamics Of Vibro Impact System

Collision vibration system is very common in daily life and engineering practice,as like coins have positive and negative,some vibration Is beneficial for us,but the others not, such as,Printer head,SHAKERS,Hammers,etc.Those colliding vibration are very beneficial for us,however those situation including excessive wear caused by some gap existing in machinery parts is bad for us.Therefor it is very important to research colliding vibration system.Collision vibration phenomena in our real life can be changed into reduced mechanical model by reasonable speculation and abstract.This article used three classic collision vibration model,and analyzed their respective dynamic behavior under the conditions of different system.First of all,This article introduced background of nonlinear vibration systems theory,then simply narrated phenomena of chaos and it’s some feature,next, introduced the status about research of collision vibration system at home and abroad and research direction in the future.After that,there set up a series of Collision vibration system which is SDOF and unilateral rigid constraints,the article focused on the researching the Poincaré map of this periodic motion,showed the process of periodic motion changing into state of chaos with the changing of system conditions.Then,article set up a series of mechanical model which is two degrees of freedom and rigid,and obtained Jacobi matrix by building Poincaré map of the system,and Obtained periodic solution by Orthogonalization and paradigm law.Finally,found the process of system changing into a chaotic state through theoretical analysis and numerical simulation.The article revealed how the main parameters of the system affect the global and bifurcation of collision vibration system,and provides a reference for optimal design of those system in daily life.In the end,article gave the model of SHAKERS which is what article focus on,after reasonable abstract and simplifying,getting it’s reduced model,and made motion analysis and stress analysis for model,and then made theoretical analysis for system’s periodic motion,solved analytical solution of the system,finally found the path where the bifurcation occurs and system enter the chaotic state.Analyzing dynamic behavior of model which can be got from engineering area by abstract,getting the path where the system enter the chaotic state by numerical simulation.Thus people can find reasonable system parameters toeffectively avoid chaos phenomenon happening.That reflected important application value of researching collision vibration system in production and life.