Dynamics Analysis Of Impact Vibration System Under The Random Factors

Impact vibration system is one of the common nonlinear dynamics systems. We oftensee the impact vibration phenomenon from the daily life and production. The study involvedin engineering mechanics, mechanical, applied physics and mathematics, and other ifelds.However, in practical engineering，whether it is elastic impact vibration system or plasticimpact vibration system, always under inlfuenced by random factors. Therefore，researchingon dynamics behavior of impact vibration system under random factors has more importantguiding signiifcance for the engineering application in the future.In this paper, we have carried on the numerical simulation for the single degree offreedom,two-single degree of freedom and double degrees of freedom elastic impact vibrationsystems as well as double degree of freedom plastic impact vibration system with the variablestep fourth order Runge-Kutta method. From bifurcation diagram can be found that in thesingle degree of freedom and double degrees of freedom elastic collision vibration systemexist in the periodic motion, the period-doubling bifurcation and chaotic motion; two-singledegree of freedom elastic impact vibration system occurs the Hopf bifurcation under theappropriate parameters; In combination with phase diagram and time response diagram, canbe see the period-doubling bifurcation and chaotic phenomenon in double degree of freedomplastic impact vibration system, but under the proper vibration frequency range, it will behappening non-conventional bifurcation. Which accompanied by grazing and strandedphenomenon at the same time.Addition random disturbance to the certainty impact vibration system, we can found thatthe random disturbance inlfuences the cycle movement of elastic impact vibration systemthrough numerical simulation and dynamic analysis, but have little inlfuence on the system’schaotic state.However^for plastic impact vibration system, when the random disturbancestrength is very small,almost has no effect on dynamics behavior of system, but with thestrength of the random disturbance, the dynamics behavior of system happen a qualitativechange under the ifxed frequency of vibration.