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CODIMENSION-2 HOPF BIFURCATION OF A TWO-DEGREE-OF-FREEDOM VIBRO-IMPACT SYSTEM

โœ Scribed by G.-L. WEN

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
312 KB
Volume
242
Category
Article
ISSN
0022-460X

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โœฆ Synopsis

Codimension-2 Hopf bifurcation problem of a two-degree-of-freedom system vibrating against a rigid surface is investigated in this paper. The four-dimensional PoincareH map of the vibro-impact system is reduced to a two-dimensional normal form by virtue of a center manifold reduction and a normal form technique. Then the theory of Hopf bifurcation of maps in R is applied to conclude the existence of codimension-2 Hopf bifurcation of the vibro-impact system. The quasi-periodic response of the system by theoretical analysis is well supported by numerical simulations. It is shown that there exists codimension-2 Hopf bifurcation in multi-degree-of-freedom vibro-impact systems. The codimension-2 tori doubling phenomenon and the routes of quasi-periodic impacts to chaos are reported brie#y.

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