Analysis Of The Influence Of Stochastic Elements Effecting To Dynamic Characteristics On The Vibro-impact Systems

Stochastic vibro-impact is an important affect to the stability and reliability of amechanical system. Three kinds of stochastic vibro-impact systems are established. Based onChebyshev Polynomial approximation, discontinuous system is transformed into continuoussystem. Based on Runge Kutta method and Monte-Carlo method, by simulating and analyzingbifurcation diagram, Poincaré section and phase diagram, the dynamic behavior of simpleharmonic excited system with stochastic disturbance and stochastic excited system are studied.Compared with the definite system, the stochastic effect on the definite system is investigated.Three kinds of stochastic vibro-impact systems are modeled. Chebyshev polynomialapproximation method is used to the systems to transform into a equal determinate system. Bynumberical method, the ERS(equal system response), the DRS(determine system response)and the SRS(stochastic system response)are simulated. Compared with each other, feasibilityof the Chebyshev polynomial approximation method in low intensity stochastic vibro-impactsystem is verified.Doubling bifurcation and three ways to the chaos of a two DOF vibro-impact systemwith single side rigid constraint is reserched. The ways to the chaos include Doublingsequence bifurcation, Neimark-Sacker bifurcation and grazing bifurcation. Randomdisturbance and narrowband noise exciting excitation are considered in the system,Monte-Carlo method is used to investigate the effect caused by low intensity stochasticelement. The effect caused by different intensity stochastic disturbance and narrowband noiseexciting is studied.The effect caused by random disturbance and narrowband noise exciting excitation to thepitchfork bifurcation of a two DOF vibro-impact system with double side rigid constraints areinvestigated, a special effort to investigate is made to study the effect caused by narrowbandnoise exciting excitation to the period-1movement in front and back of the pinchfockbifurcation point.Based on the numerical method, effect caused by low intensity stochastic element to theNeimark-Sacker bifurcation is studied. Different intensities stochastic distribute andnarrowband noise exciting are considered at the same time, the effect to periodic movement,transition of bifurcation point, the shape and the time to transformation of the fixed cycleattracter, the chaotic motion and the stability are investigated.