Two-parameter non-smooth bifurcations of period-one motions in a plastic impacting oscillator. (January 2022) - Lyu, Xiaohong; Shi, Yuqing; Luo, Guanwei
Abstract: A 2-DOF plastic impacting oscillator is considered. The discontinuity boundaries of the system phase space are defined as well as the local maps and Poincaré map. Four cases of sliding bifurcation of limit cycles in impact system are described schematically. The period-one motion modes and occurrence regions of the system are identified in the two-parameter space by numerical simulation. One-parameter bifurcation diagrams and trajectories are computed to explain the evolutions of adjacent periodic motions and the non-smooth bifurcation behaviors including grazing and four types of sliding bifurcation. Due to the discontinuous grazing bifurcation there appear a narrow hysteresis domain in the two-parameter evolution between neighboring non-impacting and impacting motions. Grazing, switching–sliding and multi-sliding bifurcations of periodic sticking motions are all manifested as rising phenomenon of the time trajectory, but the different locations of the rises in the sticking phase correspond to the different types of non-smooth bifurcations. The grazing induced dynamics and the characteristics of rising events are discussed. Notably, the codimension-2 bifurcation points are detected and investigated by numerical continuation algorithm. Highlights: Four types of sliding bifurcation in plastic impacting oscillator are computed and analyzed. Codimension-2 bifurcation points are detected and investigated. Influence of the damping ratio on dynamics in willow leaf-like region is discussed.