A perspective of the mechanisms by which energy is transferred from high- to low-frequency modes is presented. The focus is on some recent experiments that reveal how a low-amplitude high-frequency excitation can produce a large-amplitude low-frequency response. Such a phenomenon is potentially harmful, if not catastrophic. Specifically, these experiments clarify the role of internal resonances, combination external and parametric resonances, and the interactions among modes of widely spaced frequencies.
Issue Section:
Research Papers
1.
Anderson, T. J., Balachandran, B., and Nayfeh, A. H., 1992, “Observations of Modal Interactions Among Modes with Widely Spaced Frequencies,” ASME Winter Annual Meeting, Nonlinear Vibration Symposium, Anaheim, CA, November 8–13.
2.
Anderson
T. J.
Balachandran
B.
Nayfeh
A. H.
1994
, “Nonlinear Resonances in a Flexible Cantilever Beam
,” ASME Journal of Vibration and Acoustics
, Vol. 116
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.3.
Burton, T. D., and Kolowith, M., 1988, “Nonlinear Resonances with Chaotic Motion in a Flexible Parametrically Excited Beam,” Proceedings of the Second Conference on Non-Linear Vibrations, Stability, and Dynamics of Structures and Mechanisms, Blacksburg, VA, June 1–3.
4.
Cole, S., 1990, “Effects of Spoiler Surfaces on the Aeroelastic Behavior of a Low-Aspect-Ratio Rectangular Wing,” AIAA Paper No. 90-0981-CP.
5.
Cusumano, J. P., and Moon, F. C., 1990, “Low Dimensional Behavior in Chaotic Nonplanar Motions of a Forced Elastic Rod: Experiment and Theory,” in Nonlinear Dynamics in Engineering Systems, W. Schiehlen, ed., Springer-Verlag, pp. 59–66.
6.
Dugundji
J.
Mukhopadhyay
V.
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, “Lateral Bending-Torsion Vibrations of a Thin Beam Under Parametric Excitation
,” ASME Journal of Applied Mechanics
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.7.
Evan-Iwanowski, R. M., 1976, Resonance Oscillations in Mechanical Systems, Elsevier.
8.
Haddow, A. G., and Hasan, S. M., 1988, “Nonlinear Oscillations of a Flexible Cantilever: Experimental Results,” Proceedings of the Second Conference on Non-Linear Vibrations, Stability, and Dynamics of Structures and Mechanisms, Blacksburg, VA, June 1–3.
9.
Moon, F. C., 1992, Chaotic and Fractal Dynamics, Wiley.
10.
Nayfeh
A. H.
Balachandran
B.
1989
, “Modal Interactions in Dynamical and Structural Systems
,” ASME Applied Mechanics Reviews
, Vol. 42
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.11.
Nayfeh, A. H., and Balachandran, B., 1995, Applied Nonlinear Dynamics, Wiley.
12.
Nayfeh
A. H.
Chin
C.-M.
1995
, “Nonlinear Interactions in a Parametrically Excited System with Widely Spaced Frequencies
,” Nonlinear Dynamics
, Vol. 7
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.13.
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, Wiley.
14.
Nayfeh
S. A.
Nayfeh
A. H.
1993
, “Nonlinear Interactions Between Two Widely Spaced Modes—External Excitation
,” International Journal of Bifurcation and Chaos
, Vol. 3
, pp. 417
–427
.15.
Nayfeh
S. A.
Nayfeh
A. H.
1994
, “Energy Transfer from High-to Low-Frequency Modes in Flexible Structures via Modulation
,” ASME Journal of Vibration and Acoustics
, Vol. 116
, pp. 203
–207
.16.
Oh, K., and Nayfeh, A. H., 1995a, “High-to-Low Frequency Modal Interactions in a Cantilever Composite Plate,” AIAA Paper No. 95-1183.
17.
Oh, K., and Nayfeh, A. H., 1995b, “Nonlinear Combination Resonances in Cantilever Composite Plates,” submitted for publication, Journal of Vibration and Control.
18.
Oh, K., Nayfeh, A. H., and Mook, D. T., 1994, “Modal Interactions in the Forced Vibration of a Cantilever Metallic Beam,” Nonlinear and Stochastic Dynamics, ASME AMD-Vol. 192/DE-Vol. 78, pp. 237–247.
19.
Popovic, P., Nayfeh, A. H., Oh, K., and Nayfeh, S. A., 1994, “An Experimental Investigation of Energy Transfer from a High-Frequency Mode to a Low-Frequency Mode in a Flexible Structure,” Nonlinear and Stochastic Dynamics, ASME AMD-Vol. 192/DE-Vol. 78, pp. 121–133.
20.
Tabaddor, M., and Nayfeh, A. H., 1994, “Nonlinear Dynamics of a Transversely Excited Flexible Cantilever Beam,” Journal of Vibration and Acoustics, in press.
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