Global bifurcations in parametrically excited systems with zero-to-one internal resonance

Nonlinear Dynamics

Volumn 21, Issue 3, 2000, Pages 249-263

  Feng, Z C ^a,c   Liew, K M ^b,c  

^a University of Missouri   (United States)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^c Massachusetts Institute of Technology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); DEGREES OF FREEDOM (MECHANICS); EQUATIONS OF MOTION; FUNCTIONS; MATHEMATICAL MODELS;

HOMOCLINIC ORBITS; INTERNAL RESONANCE; MELNIKOV FUNCTION; PARAMETRICALLY EXCITED SYSTEMS;

RESONANCE;

EID: 0034158759     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008364914446     Document Type: Article

References (9)

1. Nayfeh, A. H. and Balachandran, B., 'Modal interactions in dynamical and structural systems', Applied Mechanics Review 42, 1989, S175-S201.
2. Anderson, T. J., Balachandran, B., and Nayfeh, A. H., 'Observations of nonlinear interactions in a flexible cantilever beam', AIAA Paper 92-2332, 1992.
3. Nayfeh, S. A. and Nayfeh, A. H., 'Nonlinear interactions between two widely spaced modes - External excitation', International Journal of Bifurcation and Chaos 3, 1993, 417-427.
4. Nayfeh, S. A. and Nayfeh, A. H., 'Energy transfer from high-to- low-frequency modes in a flexible structure via modulation', Journal of Vibration and Acoustics 116, 1994, 203-207.
5. Feng, Z. C., 'Instability caused by the coupling between nonresonant shape oscillation modes of a charged conducting drop', Journal of Fluid Mechanics 333, 1997, 1-21.
6. Feng, Z. C., 'Nonresonant modal interactions', in Proceedings of 1995 Design Engineering Technical Conference, Vol. 3 - Part A, A. K. Bajaj (ed.), ASME Press, New York, 1995, pp. 511-517.
7. Guckenheimer, J. and Holmes, P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983.
8. Nayfeh, A. H. and Chin, C-M., 'Nonlinear interactions in a parametrically excited system with widely space frequencies', Nonlinear Dynamics 7, 1995, 1-22.
9. Kovacic, G. and Wiggins, S., 'Orbits homoclinic to resonances, with an application to chaos in a model of the forced and damped Sine-Gordon equation', Physica D 57, 1992, 185-225.