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Abstract
Dynamical behaviors of a two-degree-of-freedom (TDOF) vibro-impact system are
investigated. The theoretical solution of periodic-one double-impact motion is
obtained by differential equations, periodicity and matching conditions, and the
Poincaré map is established. The dynamics of the system are studied with special
attention to Hopf bifurcations of the impact system in nonresonance, weak
resonance, and strong resonance cases. The Hopf bifurcation theory of maps in
ℝ 2 -strong
resonance is applied to reveal the existence of Hopf bifurcations of the system. The
theoretical analyses are verified by numerical solutions. The evolution from periodic
impacts to chaos in nonresonance, weak resonance, and strong resonance cases, is
obtained by numerical simulations. The results show that dynamical behavior of the
system in the strong resonance case is more complicated than that of the
nonresonance and weak resonance cases.
Keywords
Hopf bifurcation, strong resonance, quasiperiodic motion,
vibro-impact, chaos
Milestones
Received: 22 September 2005
Revised: 17 November 2005
Accepted: 25 November 2005
Published: 1 June 2006