Hostname: page-component-5cf477f64f-h6p2m Total loading time: 0 Render date: 2025-04-04T13:10:41.886Z Has data issue: false hasContentIssue false
  • English
  • Français

Reflections on Nonlinear Dynamics of Machines and Structures

Published online by Cambridge University Press:  05 May 2011

Francis C. Moon
Francis C. Moon*
Affiliation:
Department of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, U.S.A.
*
*Professor
Get access

Abstract

In this short note a comparison is made between the methodology of nonlinear analysis in machine systems versus structural systems. Because of strong nonlinearities in machines with parts in relative motion, chaotic-like dynamics are more likely to occur in complex multi-body machines than in structural systems. Furthermore, it is conjectured that well designed machines have evolved to where a small amount of chaos is always present and is sometimes desired.

Type
Articles
Information
Journal of Mechanics , Volume 16 , Issue 2 , June 2000 , pp. 79 - 83
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Bolotin, V. V., The Dynamic Stability of Elastic Systems, Holden-Day Inc. (1964).Google Scholar
2Moon, F. C. and Dowell, E. H., “The Control of Flutter Instability in a Continuous Elastic System Using Feedback,” AIAA/ASME 11th Structures, Structural Dynamics, and Materials Conference Proceedings (1970).Google Scholar
3Lee, C. K. and Moon, F. C., “Laminated Piezopolymer Plates for Torsion and Bending Sensors and Actuators,” J. Accoust. Soc. Am., pp. 2432–2439 (1989).CrossRefGoogle Scholar
4Nayfeh, A. and Mook, D., Nonlinear Oscillations, J. Wiley & Sons (1979).Google Scholar
5Pak, C. H., Nonlinear Normal Mode Dynamics, INHA University Press (1999).Google Scholar
6Holmes, P. “A Nonlinear Oscillator with a Strange Attractor,” Philos. Trans. R. Soc. London A 292, pp. 419–448 (1979).Google Scholar
7Moon, F. C., Chaotic Vibrations, J. Wiley & Sons, N.Y. (1987).Google Scholar
8Dowell, E. H. and Ilgamova, M., Studies in Nonlinear Aeroelasticity, Springer Verlag (1988).CrossRefGoogle Scholar
9Cusumano, J. P. and Moon, F. C., “Chaotic Non- Planar Vibrations of the Thin Elastica,” Journal of Sound and Vibration, 179(2), pp. 209–226 (1995).CrossRefGoogle Scholar
10Païdoussis, M. P. and Moon, F. C., “Nonlinear and Chaotic Fluid-Elastic of a Flexible Pipe Conveying Fluid,” J. Fluids & Structures, 2, pp. 567–591 (1988).CrossRefGoogle Scholar
11Thompson, J. M. T. and Virgin, L. N., “Spatial Chaos and Localization in Nonlinear Elasticity,” Physics Letters, A126, pp. 491–496 (1988).CrossRefGoogle Scholar
12El Naschie, M., “Soliton Chaos Models for Mechanical and Biological Elastic Chain.”, Physics Letters A 147, 275 (1990).CrossRefGoogle Scholar
13Pfeiffer, F., “Strange Attractors in Gear Transmissions,” Ingenieur Archiv, 58, pp. 113–125 (1988).CrossRefGoogle Scholar
14True, H., “Nonlinear Railway Dynamics,” in 1st European Nonlinear Oscillations Conference Proceedings, Kreuzer, E., Schmidt, G. Ed., Akademie Verlag (1998).Google Scholar
15Grabec, I., “Chaos Generated by the Cutting Process,” Physics Letters, A 117, 384 (1986).CrossRefGoogle Scholar
16Popp, K. and Stelter, P., “Nonlinear Oscillations of Structures Induced by Friction,” in Nonlinear Dynamics in Engineering Systems, Schiehlen, W., Ed. Springer Verlag, pp. 233–240 (1990).CrossRefGoogle Scholar
17Peterka, F., “Bifurcations and Transition Phenomena in an Impact Oscillator,” Solitons & Fractals, 7(10), pp. 1635–1647 (1996).CrossRefGoogle Scholar
18Glocker, Ch., “The Principles of d'Alembert, Jourdain, and Gauss Nonsmooth Dynamic.” ZAMM (1999).Google Scholar
19Goldberger, A. L., et al., “Chaos and Fractal in Human Physiology,” Scientific American, 262(2), pp. 42–49 (1990).CrossRefGoogle ScholarPubMed
20Reuleaux, F., Theoretical Kinematics, translated as The Kinematics of Machinery, published in reprint form by Dover Publ. Inc., N.Y., 1963 (1876).Google Scholar
21Suh, N, The Principles of Design, Oxford University Press (1990).Google Scholar
22Moon, F. C. Ed., Dynamics and Chaos in Manufacturing Processes, J. Wiley, N.Y. (1998).Google Scholar
23Pao, Y. H., Keh, D. C. and Howard, S. M., “Dynamic Response and Waves in Plane Trusses and Frames,” AIAA Journal, 37(5), pp. 594–603 (1999).CrossRefGoogle Scholar
24Vakakis, A. F., Normal Modes and Localization in Nonlinear Systems, J. Wiley & Sons, NY (1996).CrossRefGoogle Scholar