Abstract
In this paper we consider a class of systems for which motions are possible in which a small number of modes undergo chaotic oscillations while the remaining modes, if started with zero energy, remain at a zero energy state for all time. Of interest here is the local stability of these modes, which are parametrically driven by the active modes. We specify the class of systems to be considered, present a general stability result, and then sketch the analysis and results for a specific mechanical device. Details of the results can be found in Reference [1].
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References
S.R. Hsieh and S.W. Shaw, 1990, Journal of Sound and Vibration 138, 421–431. The stability of modes at rest in a chaotic system.
E. F. Infante, 1968, American Society of Mechanical Engineers Journal of Applied Mechanics 35, 7–12. On the stability of some linear nonautonomous random systems.
V. Brunsden, J. Cottrel and P. Holmes, 1989, Journal of Sound and Vibration 130, 1–25. Power spectra of chaotic vibrations of a buckled beam.
V. Brunsden and P. Holmes, 1987, Physical Review Letters 58, 1699–1702. Power spectra of strange attractors near homoclinic orbits.
A.K. Bajaj, 1990, Preprint, Department of Mechanical Engineering, Purdue University, Complex dynamics of whirling strings.
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© 1991 Birkhäuser Verlag Basel
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Shaw, S.W., Hsieh, SR. (1991). The Local Stability of Inactive Modes in Chaotic Multi-Degree-of-Freedom Systems. In: Seydel, R., Schneider, F.W., Küpper, T., Troger, H. (eds) Bifurcation and Chaos: Analysis, Algorithms, Applications. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 97. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7004-7_43
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DOI: https://doi.org/10.1007/978-3-0348-7004-7_43
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7006-1
Online ISBN: 978-3-0348-7004-7
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