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HOPF BIFURCATION OF A TWO-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM

✍ Scribed by G.-W. Luo; J.-H. Xie

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
321 KB
Volume
213
Category
Article
ISSN
0022-460X

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✦ Synopsis

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 PoincareΒ΄map of the vibro-impact system to a two-dimensional one, and then the theory of Hopf bifurcation of maps in R 2 is 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 PoincareΒ΄sections, is obtained by numerical simulations, and routes of quasi-periodic impacts to chaos are stated briefly.

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