Nonlinear Vibration Modes of Parametrically Coupled Self-Excited Oscillators

• Autorzy: Warmiński J.
• Języki publikacji: EN

Abstrakty

EN

A technique for determination of vibration modes of nonlinear coupled parametrically self excited oscillators is presented in the paper. The method is applied for vibration regions ii which the synchronisation phenomenon takes place and the system vibrates with singli frequency. The, so called, resonant Nonlinear Normal Modes (NNM) are determined inside these resonance regions. The NNMs are defined on the basis of natural vibrations o a nonlinear system, as nonlinear functions of amplitude. Correctness of the results ii verified by direct numerical simulations.

Słowa kluczowe

EN

nonlinear vibrations; nonlinear normal modes; self-excitation; parametric resonance

PL

drgania nieliniowe; ruchy chaotyczne; samowzbudzenia; rezonans parametryczny

• Wydawca: Oficyna Wydawnicza Politechniki Warszawskiej
• Czasopismo: Machine Dynamics Problems
• Rocznik: 2008
• Tom: Vol. 32, No. 4
• Strony: 107--118
• Opis fizyczny: Bibliogr. 10 poz., wykr.

Twórcy

autor

Warmiński J.

• Lublin University of Technology. Department of Applied Mechanics,

Bibliografia

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• Nayfeh, A. H., 1981, Introduction to Perturbation Technique, Wiley, New York
• Rega, G., (Ed.), 2009, Nonlinear Normal Modes, Dimension Reduction and Localization in Vibrating Systems, EUROMECH 503, Frascati (Rome), Italy, 27 September - 2 October 2009 (will appear).
• Rosenberg, R. M., 1960, Normal Modes of Non-linear Dual-Mode Systems, Journal of Applied Mechanics, Ser. E, 27, No 2, 263-268.
• Shaw, S. W., Pierre, C., 1993, Normal Modes for Non-Linear Vibratory Systems, Journal of Sound and Vibrations, 164(1), 85-124.
• Szemplińska-Stupnicka, W., 1977, One-modal Analysis of Resonant Vibrations of Nonlinear Systems, Institute of Fundamental Research (IPPT) of Polish Academy of Sciences (PAN), 22/197.
• Vakakis, A. (Ed.), 2006, Nonlinear Normal Modes and Localization in Vibrating Systems, Samos, Greece, Conference Proceedings.
• Vakakis, A. F., 1997, Non-Linear Normal Modes (NNMs) and Their Applications in Vibration Theory: an Overview, Mechanical Systems and Signal Processing, 11(1), 3-22.
• Warmiński, J., 2001, Regular and Chaotic Vibrations of Parametrically and Self-Excited Systems with Ideal and Non-Ideal Energy Sources, Technical University of Lublin Publisher, Lublin, Poland (in Polish).
• Warmiński, J., 2008, Nonlinear normal modes of Coupled self-excitation oscillators in regular and chaotic vibration regimes. Journal of Theoretical and Applied Mechanics, 46, No 4, 693-714.