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BRIEF NOTES

Period-Doubling Bifurcation and Non-Typical Route to Chaos of a Two-Degree-Of-Freedom Vibro-Impact System

[+] Author and Article Information
G. L. Wen, J. H. Xie

Department of Applied Mechanics and Engineering, Southwestern Jiaotong University, Chengdu 610031, P. R. China

J. Appl. Mech 68(4), 670-674 (Dec 05, 2000) (5 pages) doi:10.1115/1.1379035 History: Received April 02, 2000; Revised December 05, 2000
Copyright © 2001 by ASME
Topics: Bifurcation , Chaos , Motion
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References

Shaw,  J., and Shaw,  S. W., 1989, “The Onset of Chaos in a Two-degree-Freedom Impacting System,” ASME J. Appl. Mech., 56, pp. 168–174.
Luo,  G. W., and Xie,  J. H., 1998, “Hopf Bifurcation of a Two-Degree-of-Freedom Vibrato Impact System,” J. Sound Vib., 213, No. 3, pp. 391–408.
Xie,  J. H., 1996, “Codimension Two Bifurcations and Hopf Bifurcations of an Impacting Vibrating System,” Appl. Math. Mech., 17, pp. 65–75.
Car, J., 1981, Applications of Center Manifold Theory (Applied Mathematical Sciences 35), Springer-Verlag, New York, pp. 33–36.
Iooss, G., 1987, Forms normales d’applications: Caractérisation globale et méthode de calcul, Universite de Nice, Nice, France.
Elphick,  C., Tirapegui,  E., Brachet,  M., Coullet,  P., Iooss,  G., 1987, “A Simple Global Characterization for Normal Forms of Singular Vector Fields,” Physica D, 29, pp. 95–127.

Figures

Grahic Jump Location
v=0.75, stable period 2 fixed points
Grahic Jump Location
v=0.7554, stable period 4 fixed points
Grahic Jump Location
v=0.7563, four stable Hopf circles
Grahic Jump Location
v=0.75685, four stable 2T-torus
Grahic Jump Location
v=0.7515, stable period 2 fixed points
Grahic Jump Location
v=0.754, stable period 4 fixed points
Grahic Jump Location
v=0.7552, four stable Hopf circles
Grahic Jump Location
v=0.755965, phase locking

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