Dynamical analysis of a two-parameter family for a vibro-impact system in resonance cases

Journal of Sound and Vibration

Volumn 287, Issue 1-2, 2005, Pages 101-115

  Ding, Wangcai ^a   Xie, Jianhua ^b  

^a LANZHOU JIAOTONG UNIVERSITY   (China)

^b SOUTHWEST JIAOTONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BIFURCATION (MATHEMATICS); CHAOS THEORY; COMPUTER SIMULATION; CONFORMAL MAPPING; DEGREES OF FREEDOM (MECHANICS); EIGENVALUES AND EIGENFUNCTIONS; HARMONIC ANALYSIS; MATHEMATICAL MODELS; RESONANCE; VECTORS;

HOPF BIFURCATION; PERIODIC MOTIONS; SUBHARMONIC BIFURCATION; VIBRO-IMPACT SYSTEMS;

VIBRATORS;

EID: 22344457193     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2004.10.035     Document Type: Article

References (20)

1. P.J. Holmes The dynamics of repeated impacts with a sinusoidally vibrating table Journal of Sound and Vibration 84 2 1982 173 189
2. J.M.T. Thompson Chaos after period-doubling bifurcations in the resonance of an impact oscillator Physics Letters 91A 1983 5 8
3. S.W. Shaw, and P.J. Homles Periodically forced linear oscillator with impacts chaos and long-period motions Physical Review Letters 51 8 1983 623 626
4. G.S. Whiston Singularities in vibro-impact dynamics Journal of Sound and Vibration 152 3 1992 427 460
5. A.P. Ivanov Stabilization of an impact oscillator near grazing incidence owing to resonance Journal of Sound and Vibration 162 3 1993 562 565
6. A.B. Nordmark Non-periodic motion caused by grazing incidence in an impact oscillator Journal of Sound and Vibration 145 2 1991 279 297
7. G.W. Luo, and J.H. Xie Hopf bifurcations of a two-degree-of-freedom vibro-impact system Journal of Sound and Vibration 213 3 1998 391 480
8. J.H. Xie Codimension two bifurcations and Hopf bifurcations of an impacting vibrating system Applied Mathematics and Mechanics 17 1 1996 65 75
9. G.L. Wen Codimension-2 Hopf bifurcation of a two-degree-of-freedom vibro-impact system Journal of Sound and Vibration 242 3 2001 475 485
10. G.L. Wen, and J.H. Xie Period-doubling bifurcation and non-typical route to chaos of a two-degree-of-freedom vibro-impact system Journal of Applied Mechanics 68 4 2001 670 674
11. G. Iooss, Bifurcation of maps and applications, Mathematics Studies, vol. 36, North-Holland, Amsterdam, 1979.
12. A. Chenciner, and G. Iooss Bifurcation de torus invariant Archive for Rational Mechanics and Analysis 69 1979 109 198
13. Y.H. Wan Bifurcation into invariant tori at points of resonance Archive for Rational Mechanics and Analysis 68 1978 343 357
14. V.I. Arnold Geometrical Methods in the Theory of Ordinary Differential Equations 1983 Springer Berlin
15. V.I. Arnold Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields Funktsional nvi Analiz i ego Prilozheniya 11 2 1977 1 10
16. G.W. Luo, and J.H. Xie Hopf bifurcations and chaos of a two-degree-of-freedom vibro-impact system in two strong resonance cases International Journal of Non-linear Mechanics 37 1 2002 19 34
17. F.S. Berezovskaia, and A.I. Khibnik On the bifurcations of seperatrices in the problem of stability loss of auto-oscillations near 1:4 resonance Prikladnaya Matematika Mekhanika 44 1980 663 667
18. B. Krauskopf Bifurcation sequences at 1:4 resonance an inventory Nonlinearity 7 1994 1073 1091
19. B. Krauskopf The bifurcation set for the 1:4 resonance problem Experimental Mathematics 3 2 1995 107 128
20. J. Carr, Applications of Center Manifold Theory, Applied Mathematical Sciences, vol. 35, Springer, Berlin, 1981, pp. 33-36.