Study on transition of coexisting attractors in a piecewise smooth system

A two-degree-of-freedom vibro-impact system with clearance is researched in this study, and the formation and transition characteristics of coexisting attractors are investigated using the shooting method and the parameter continuation algorithm. The Poincaré mapping analysis method and Floquet theory are employed, and a switching matrix is introduced, through which the Jacobian matrix corresponding to the Poincaré mapping is obtained. The distribution of coexisting attractors between adjacent periodic motions is determined using the parameter continuation algorithm, and the stability of these coexisting attractors is analyzed in combination with the shooting method. The coexistence and transition of the attractor induced by bifurcation behaviors are analyzed. It is found that grazing bifurcation in such systems occurs continuously, while the coexistence of attractors can be led to by saddle-node grazing bifurcation and pitchfork bifurcation. Additionally, chaotic attractors can be made to disappear suddenly due to the boundary crisis. The findings of this study can be used as a reference for the parameter design, vibration reduction optimization, and dynamic control of mechanical vibration systems with clearance.