Abstract
A three-degree-of-freedom vibro-impact system is considered. The nonlinear dynamical model and the six-dimensional Poincaré map are established and the dynamical behaviors of the system, including double Neimark–Sacker bifurcation, torus T 2 and its routes to chaos, is investigated by numerical simulations. As the control parameters vary, the torus T 2 changes into multi-circle torus T 1 via one-frequency phase locking on its position, which are divided into longitude circles and latitude circles, and the system keeps quasi-periodic motion. Further the impact motion settles into periodic orbit via two-frequency phase locking, then the system leads eventually to chaos. The second route to chaos shows, by establishing the secondary Poincaré section, that the torus T 2 leads to chaos via torus doubling bifurcation and there may exist torus doubling cascade.
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