Hopf bifurcation of a two-degree-of-freedom vibro-impact system

Journal of Sound and Vibration

Volumn 213, Issue 3, 1998, Pages 391-408

  Luo, G W ^a   Xie, J H ^b  

^a LANZHOU JIAOTONG UNIVERSITY   (China)

^b SOUTHWEST JIAOTONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000760062     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jsvi.1997.1361     Document Type: Article

References (32)

1. E. H. DOWELL 1982 Journal of Sound and Vibration 85, 333-344. Flutter of a buckled plate as an example of chaotic motion of a deterministic autonomous system.
2. S. W. SHAW and P. J. HOLMES 1983 Journal of Sound and Vibration 90, 129-155. A periodically forced piecewise linear oscilinear.
3. J. M. T. THOMPSON 1883 Proceedings of the Royal Society of London A387, 407-427. Complex dynamics of compliant offshore structures.
4. S. W. SHAW and P. J. HOLMES 1983 Journal of Applied Mechanics 50, 894-857. A periodically forced impact oscillator with large dissipation.
5. S. W. SHAW 1985 Journal of Applied Mechanics 52, 453-646. The dynamics of a harmonically excited system having rigid amplitude constraints.
6. G. S. WHISTON 1987 Journal of Sound and Vibration 115, 303-319. The vibro-impact response of a harmonically excited and preloaded one-dimensional linear oscillator.
7. G. S. WHISTON 1987 Journal of Sound and Vibration 118, 395-429. Global dynamics of a vibro-impact oscillator.
8. A. B. NORDMARK 1991 Journal of Sound and Vibration 145, 279-297. Non-periodic motion caused by grazing incidence in an impact oscillator.
9. G. S. WHISTON 1992 Journal of Sound and Vibration 152, 427-460. Singularities in vibro-impact dynamics.
10. S. NSATSIAVA and H. GONZALEZ 1992 Journal of Applied Mechanics 59, 284-290. Vibration of harmonically excited oscillators with asymmetric constraints.
11. F. PETERKA and J. VCACIK 1992 Journal of Sound and Vibration 154, 95-115. Transition to chaotic motion in mechanically stems with impacts.
12. L. ZUO and A. CURNIER 1994 Journal of Sound and Vibration 174, 289-313. Non-linear real and complex modes of conewise linear systems.
13. S. NARAYANAN and P. SEKAR 1995 Journal of Sound and Vibration 184, 281-298. Periodic and chaotic responses of sdf system with piecewise linear stiffness subjected to combined harmonic and flow induced excitations.
14. C. BUDD and F. DUX 1995 Journal of Sound and Vibration 184, 475-502. The effect of frequency and clearance variations on single-degree-of-freedom impact oscillators.
15. J.-H. XIE 1996 Applied Mathematics and Mechanics 17, 65-75. Codimension two bifurcations and hopf bifurcations of an impacting vibrating system.
16. C. N. BAPAT and C. BAPAT 1988 Journal of Sound and Vibration 120, 53-61. Impact-pair under periodic excitation.
17. M. S. HEIMAN, A. K. BAJAJ and P. J. SHERMAN 1988 Journal of Sound and Vibration 124, 55-78. Periodic motions and bifurcations in dynamics of an inclined impact pair.
18. J. E. KOZOL and R. M. BRACH 1991 Journal of Sound and Vibration 148, 319-327. Two-dimensional vibratory impact and chaos.
19. Z.-Z. SHU 1991 Acta Mechanica Sinica 7(4), 369-375. Motion types and chaos of multi-body systems vibrating with impacts.
20. C. K. SUNG and W. S. YU 1992 Journal of Sound and Vibration 158, 317-329. Dynamics of harmonically excited impact damper: bifurcations and chaotic motion.
21. J. O. AIDANPAA and R. B. GUPTA 1993 Journal of Sound and Vibration 165, 305-327. Periodic and chaotic behaviour of a threshold-limited two-degree-of-freedom system.
22. S. NATSIAVAS 1993 Journal of Sound and Vibration 165, 439-453. Dynamics of multiple-degree-of-freedom oscillators with colliding components.
23. A. P. IVANON 1993 Journal of Sound and Vibration 178, 361-378. Impact oscillations: linear theory of stability and bifurcations.
24. R. P. S. HAN and A. C. J. LUO 1995 Journal of Sound and Vibration 181, 231-250. Chaotic motion of a horizontal impact pair.
25. C. N. BAPAT 1995 Journal of Sound and Vibration 184, 417-427. The general motion of an inclined impact damper with friction.
26. B. D. HASSARD, N. D. KAZARINOFF and Y.-H. WAN Theory and Applications of Hopf Bifurcation. Cambridge: Cambridge University Press.
27. J. CAR Applications of Centre Manifold Theory. Applied Mathematical Sciences 35. Berlin: Springer-Verlag.
28. G. Iooss Bifurcation of Maps and Applications. Mathematics Studies 36. Amsterdam: North-Holland. See pp. 201-222.
29. O. E. LANDFORD 1973 Bifurcation of Periodic Solution into Invariant Tori: the Work of Ruelle and Takrns. Lecture Notes in Mathematics. Berlin: Springer-Verlag.
30. 2.
31. K. KANEKO 1984 Progress of Theoretical Physics 72, 202-215. Oscillation and doubling of torus.
32. A. ARNEODO, P. H. COULLET and E. A. SPIEGEL 1983 Physics Letters 94A, 1-6. Cascade of period doublings of tori.