A two-degrees-of-freedom vibratory system with a clearance or gap is under con- sideration based on the Poincaré map.Stability and local bifurcation of the period-one double- impact symmetrical motion of the syst...A two-degrees-of-freedom vibratory system with a clearance or gap is under con- sideration based on the Poincaré map.Stability and local bifurcation of the period-one double- impact symmetrical motion of the system are analyzed by using the equation of map.The routes from periodic impact motions to chaos,via pitchfork bifurcation,period-doubling bifurcation and grazing bifurcation,are studied by numerical simulation.Under suitable system parameter con- ditions,Neimark-Sacker bifurcations associated with periodic impact motion can occur in the two-degrees-of-freedom vibro-impact system.展开更多
Stability and dynamic characteristics of a bail bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different clearance values are assumed to calculate the nonlinear stability ...Stability and dynamic characteristics of a bail bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different clearance values are assumed to calculate the nonlinear stability of periodic solution with the aid of the Flo- quet theory. Bifurcation and chaos behavior are analyzed with variation of the clearance and rotational speed. It is found that there are three routes to unstable periodic solution. The period-doubling bifurcation and the secondary Hopf bifurcation are two usual routes to instability. The third route is the boundary crisis, a chaotic attractor occurs suddenly as the speed passes through its critical value. At last, the instable ranges for different internal clearance values are described. It is useful to investigate the stability property of ball bearing rotor system.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos.10172042 and 10072051)Science Foundation of Education Ministry of China for Ph.D Programmes (No.20010613001).
文摘A two-degrees-of-freedom vibratory system with a clearance or gap is under con- sideration based on the Poincaré map.Stability and local bifurcation of the period-one double- impact symmetrical motion of the system are analyzed by using the equation of map.The routes from periodic impact motions to chaos,via pitchfork bifurcation,period-doubling bifurcation and grazing bifurcation,are studied by numerical simulation.Under suitable system parameter con- ditions,Neimark-Sacker bifurcations associated with periodic impact motion can occur in the two-degrees-of-freedom vibro-impact system.
基金Project supported by the National Natural Science Foundation of China (No.50275113) and the Doctoral Science Foundation of Ministry of Education (No.20030698017)
文摘Stability and dynamic characteristics of a bail bearing-rotor system are investigated under the effect of the clearance in the ball bearing. Different clearance values are assumed to calculate the nonlinear stability of periodic solution with the aid of the Flo- quet theory. Bifurcation and chaos behavior are analyzed with variation of the clearance and rotational speed. It is found that there are three routes to unstable periodic solution. The period-doubling bifurcation and the secondary Hopf bifurcation are two usual routes to instability. The third route is the boundary crisis, a chaotic attractor occurs suddenly as the speed passes through its critical value. At last, the instable ranges for different internal clearance values are described. It is useful to investigate the stability property of ball bearing rotor system.
