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2013•Engineering MechanicsRequires access

COLLISION PROBLEM OF A FOUT-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM

Wanxian Li

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Abstract

A mathematical model of a four-degree-of-freedom vibro-impact system is established,deriving the eight-dimensional Poincare maps of periodic motion in the system,calculating the centre manifold and showing the steps for the reduction of high-dimensional maps to a two-dimensional one.The stability of periodic motion is studied,the Hopf bifurcation and period-doubling bifurcation phenomena of periodic motion in the system are analyzed based on the suitable parameter combination,and the existence of the Hopf bifurcation is verified in a four-degree-of-freedom vibro-impact system.The evolution process of the system to chaos and the system invariant torus are simulated numerically.Consequently,the formation process of instability and chaos of invariant torus in the vibro-impact system are revealed.

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What this paper is about

A mathematical model of a four-degree-of-freedom vibro-impact system is established,deriving the eight-dimensional Poincare maps of periodic motion in the system,calculating the centre manifold and showing the steps for the reduction of high-dimensional maps to a two-dimensional one.The stability of periodic motion is studied,the Hopf bifurcation and period-doubling bifurcation phenomena of periodic motion in the system are analyzed based on the suitable parameter combination,and the existence of the Hopf bifurcation is verified in a four-degree-of-freedom vibro-impact system.The evolution process of the system to chaos and the system invariant torus are simulated numerically.Consequently,the formation process of instability and chaos of invariant torus in the vibro-impact system are revealed.

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Available abstract

A mathematical model of a four-degree-of-freedom vibro-impact system is established,deriving the eight-dimensional Poincare maps of periodic motion in the system,calculating the centre manifold and showing the steps for the reduction of high-dimensional maps to a two-dimensional one.The stability of periodic motion is studied,the Hopf bifurcation and period-doubling bifurcation phenomena of periodic motion in the system are analyzed based on the suitable parameter combination,and the existence of the Hopf bifurcation is verified in a four-degree-of-freedom vibro-impact system.The evolution process of the system to chaos and the system invariant torus are simulated numerically.Consequently,the formation process of instability and chaos of invariant torus in the vibro-impact system are revealed.

Key concepts: Hopf bifurcation, Mathematics, Bifurcation, Period-doubling bifurcation, Torus, Instability, Invariant (physics), Poincaré map

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COLLISION PROBLEM OF A FOUT-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM — Research Paper | ScholarLens