Vol. 1, No. 2, 2006

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Nonlinear dynamic characteristics of a vibro-impact system under harmonic excitation

Jianlian Cheng and Hui Xu

Vol. 1 (2006), No. 2, 239–258
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