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BIFURCATION AND CHAOS OF A THREE DEGREES-OF-FREEDOM SYSTEM WITH CLEARANCE

Yong Hua Zhou

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Abstract

An important field in vibration engineering is the dynamics of mechanical systems with clearance and constraint.A three degrees-of-freedom system with a pair of symmetric set-up elastic stops is considered in this paper.The differential equation of the system motion is derived and the Poincare map is established numerically.Bifurcations and chaos of the system are investigated by numerical simulations and analytical method.The routes from quasi-periodic,period-doubling with Neimark-Sarker bifurcation,period-doubling with pitchfork bifurcation,to chaos,are discussed,respectively.It is shown that some routes to chaos in the three degrees-of-freedom system are non-typical.It is possible to optimize the parameters of the practical system by investigation of bifurcation and chaos.

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What this paper is about

An important field in vibration engineering is the dynamics of mechanical systems with clearance and constraint.A three degrees-of-freedom system with a pair of symmetric set-up elastic stops is considered in this paper.The differential equation of the system motion is derived and the Poincare map is established numerically.Bifurcations and chaos of the system are investigated by numerical simulations and analytical method.The routes from quasi-periodic,period-doubling with Neimark-Sarker bifurcation,period-doubling with pitchfork bifurcation,to chaos,are discussed,respectively.It is shown that some routes to chaos in the three degrees-of-freedom system are non-typical.It is possible to optimize the parameters of the practical system by investigation of bifurcation and chaos.

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Available abstract

An important field in vibration engineering is the dynamics of mechanical systems with clearance and constraint.A three degrees-of-freedom system with a pair of symmetric set-up elastic stops is considered in this paper.The differential equation of the system motion is derived and the Poincare map is established numerically.Bifurcations and chaos of the system are investigated by numerical simulations and analytical method.The routes from quasi-periodic,period-doubling with Neimark-Sarker bifurcation,period-doubling with pitchfork bifurcation,to chaos,are discussed,respectively.It is shown that some routes to chaos in the three degrees-of-freedom system are non-typical.It is possible to optimize the parameters of the practical system by investigation of bifurcation and chaos.

Key concepts: Bifurcation, Pitchfork bifurcation, Period-doubling bifurcation, Degrees of freedom (physics and chemistry), Saddle-node bifurcation, Mathematics, Biological applications of bifurcation theory, Vibration

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BIFURCATION AND CHAOS OF A THREE DEGREES-OF-FREEDOM SYSTEM WITH CLEARANCE — Research Paper | ScholarLens