Stability and Bifurcation of Gear System Coexistence Attractors
A 3-DOF gear system is studied.The multi-initial bifurcation diagrams of the system are obtained through numerical simulation.The influence of the damping coefficient on the dynamic characteristics of the system is analyzed in combination with the Top Lyapunov Exponent(TLE)diagrams.The stability and bifurcation of the coexisting attractor are studied by applying numerical simulation,continuation shooting method and Floquet characteristic multiplier.The cell map-ping method is applied to calculate the basins of attraction of the coexisting attractors,and the bifurcation diagrams,phase di-agrams and Poincaré mapping are combined to reveal the erosion and evolution process of the basin of attraction of the coex-isting attractors with the change of system parameters.The results show that the distance between the period-doubling bifur-cation and the saddle-node bifurcation in the system is quite short,and the saddle-node bifurcation causes the final state of the system to jump between two different periodic motions,leading to the sub-critical feature of the period-doubling bifurca-tion.It is also found that the coexisting periodic attractors are mainly caused by the saddle-node bifurcation,and the periodic attractors coexist with quasi-periodic attractors if the saddle-node bifurcation occurs in the quasi-periodic motion interval.
vibration and wavegear systemFloquet multipliercoexisting attractorsstability
万方数据
维普
