Bifurcation and stability of coexistence attractors in a time-varying stiffness impact vibration system
WANG Xin
KANG Kai
JIN Hua
Abstract：Considering the time-varying stiffness characteristics of mechanical systems,a single-degree-of-freedom time-varying impact vibration system model with clearance stiffness was studied.The dynamic model and Poincaré map were established,and numerical calculation methods were given.The influence of the ratio of time-varying stiffness amplitudes on the dynamic response and characteristics of the system was analyzed using numerical simulation and the maximum Lyapunov exponent.By combining multiple initial value bifurcation diagrams,attraction domains,phase diagrams,and Poincaré mapping diagrams,the evolution and bifurcation of coexisting attractors in the system were studied by applying the continuation shooting method.When the bifurcation parameter changes and the system exhibits the coexistence phenomenon,the reasons for the appearance and disappearance of local attractors and the distribution mechanism of unstable attractors in the attraction domain before and after bifurcation are revealed.The stability change rule of coexisting attractors is obtained.
Keywords：Time-varying stiffnessVibration systemCoexistence attractorStabilityBifurcation
Publication Date：2025-10-15
Online Publishing Date：2026-09-12(First online date of this platform, not the publication date of the document)
Pages：8( 43-50 )