1. HOPF BIFURCATION OF A TWO-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM
- Author
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G.-W. Luo, J.H. Xie, Department of Mechanical Engineering, Lanzhou Railway Institute, Department of Applied Mechanics and Engineering, and Southwest Jiaotong University (SWJTU)
- Subjects
Period-doubling bifurcation ,Hopf bifurcation ,[PHYS.MECA.VIBR]Physics [physics]/Mechanics [physics]/Vibrations [physics.class-ph] ,Acoustics and Ultrasonics ,Mechanical Engineering ,Mathematical analysis ,Saddle-node bifurcation ,Geometry ,Condensed Matter Physics ,Bifurcation diagram ,symbols.namesake ,Transcritical bifurcation ,Bifurcation theory ,Pitchfork bifurcation ,Mechanics of Materials ,symbols ,Bogdanov–Takens bifurcation ,Mathematics - Abstract
International audience; The bifurcation problem of a two-degree-of-freedom system vibrating against a rigid surface is studied in this paper. It is shown that there exist Hopf bifurcations in the vibro-impact systems with two or more degrees of freedom under suitable system parameters. In the paper, a centre manifold theorem technique is applied to reduce the Poincaré map of the vibro-impact system to a two-dimensional one, and then the theory of Hopf bifurcation of maps inR2is applied to conclude the existence of Hopf bifurcation of the vibro-impact system. The theoretical solutions are verified by numerical computations. The quasi-periodic response of the system, represented by invariant circles in the projected Poincaré sections, is obtained by numerical simulations, and routes of quasi-periodic impacts to chaos are stated briefly.
- Published
- 1998
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