Regular and chaotic vibrations of a parametrically and self-excited system under internal resonance condition

Meccanica

Volumn 40, Issue 2, 2005, Pages 181-202

  Warminski, Jerzy ^a  

^a LUBLIN UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Chaos; Internal resonance; Parametric vibrations; Self excitation; Synchronisation

Indexed keywords

CHAOS THEORY; DEGREES OF FREEDOM (MECHANICS); NATURAL FREQUENCIES; OSCILLATORS (ELECTRONIC); RESONANCE; SYNCHRONIZATION;

INTERNAL RESONANCE; PARAMETRIC VIBRATIONS; SELF-EXCITATION;

MOLECULAR VIBRATIONS;

EID: 23744500168     PISSN: 00256455     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11012-005-3306-4     Document Type: Article

References (25)

1. Awrejcewicz, J., Bifurcation and Chaos. Theory and Application, Springer Verlag, Berlin, 1994.
2. Kapitaniak, T. and Steeb, W.H., 'Transition to hyperchaos in coupled generalized Van der Pol's equations', Phys. Lett. A 152 (1991) 33-37.
3. Kononenko, W.O. and Kovalchuk, P., 'Influence of parametric excitation on self-excited system', Prikladnaja Mechanika, Nauka, Glawnaja Redakcja Fiziko-Matiematiczeskoj Literatury 7(6) (1971) 3-10. (Moscow)
4. Tondl, A., On the Interaction between Self-excited and Parametric Vibrations, Monographs and Memoranda, No.25, National Research Institute for Machine Design, Prague, 1978.
5. Warminski, J., 'Synchronisation effects and chaos in van der Pol-Mathieu oscillator', J. Theo. Appl. Mech. 4(39) (2001a) 861-884.
6. Szabelski, K. and Warminski, J., 'Vibrations of a non-linear self-excited system with two degrees of freedom under external and parametric excitation', J. Nonlinear Dyn. 14 (1997) 23-36.
7. Warminski, J., Litak, G. and Szabelski, K., 'Synchronisation and chaos in a parametrically and self-excited system with two degrees of freedom', J. Nonlinear Dyn. 22 (2000) 135-153.
8. Szabelski, K., and Warminski, J., 'The parametric self excited non-linear system vibrations analysis with the inertial excitation', Int. J. Non-Linear Mech. 30(2) (1995a) 179-189.
9. Szabelski, K., and Warminski, J., 'The self-excited system vibrations with the parametric and external excitations', J. Sound Vib. 187(4) (1995b) 595-607.
10. Warminski, J., Regular and Chaotic. Vibrations of Self- and Parametrically Excited Systems with Ideal and Non-Ideal Energy Sources (in Polish), Lublin University of Technology Publishers, Lublin, Poland, 2001b.
11. Warminski, J., 'Influence of external force on the parametric and self-excited system', J. Tech. Phys. 42 (2001 a) 349-366.
12. Warminski, J., 'Regular, chaotic and hyperchaotic vibrations of nonlinear systems with self, parametric and external excitations', Sci. J. FACTA UNIVERSITATIS 3(14) (2003a) 891-905.
13. Warminski, J., Balthazar, J.M., and Brasil, R.M.L.R.F., 'Vibrations of non-ideal parametrically and self-excited model', J. Sound Vib. 245(2) (2001) 363-374.
14. Warminski, J., 'Complexity and chaos of parametrically and self-excited system with non-ideal energy source', In Matthew P.C. (ed.), Modern Practice in Stress and Vibration Analysis, pp. 363-370 ttp Trans Tech Publications, Materials Science Forum, Switzerland, Germany, UK, USA, 2003b.
15. Bajkowski, J., and Szemplinska-Stupnicka, W., 'Internal resonances effects - simulation versus analytical methods results', J. Sound Vib. 104(2) (1986) 259-275.
16. Bajkowski, J., Internal Resonaces in Nonlinear Vibrating Systems, Part I (in Polish), Institute of Fundamental Technological Research, Polish Academy of Sciences, IPPT PAN, No. 15, Warsaw, 1984.
17. Warminski, J., Litak, G., Cartmell, M.P., Khanin, R., and Wiercigroch, M., 'Approximate analytical solutions to the nonlinear primary metal cutting process', J. Sound Vib. 259(4) (2003) 917-933.
18. Ishida, Y., and Inoue, T., 'Nonstationary oscillations of a nonlinear rotor during acceleration through the majar critical speed - Influence of internal resonance', JSME Int. J. Series C-Mech. Sys. Machine Elements Manufacturing 41(3) (1998) 599-607.
19. Rusinek, R., Szabelski, K. and Warminski, J., 'Influence of the workpiece profile on the self-excited vibrations in metal turning process', In Radons, G. and Neugebauer, R., (ed.), Nonlinear Dynamics of Production Systems, Wiley-VCH, 2004, pp. 153-167.
20. Schmidt G., Interaction of self-excited, forced and parametrically excited vibrations, Applications of the Theory of Nonlinear Oscillations - The 9th International Conference on Non-Linear Oscillations, Naukova Dumka, Kiev, 1984, pp. 310-315.
21. Luongo, A., Paolone, A., and Piccardo, G., 'Postcritical behavior of cables undergoing two simultaneos galloping modes', MECCANICA Int. J. Italian Assoc. Theo. Appl. Mech. 33(3) (1998) 229-242.
22. Lacarbonara, W., Rega, G. and Nayfeh, A.H., 'Resonant nonlinear normal modes. Part I: Analytical treatment for one-dimensional structural systems', Int. J. Non-Linear Mech. 38 (2003) 851-872.
23. Lacarbonara, W. and Rega, G., 'Resonant nonlinear normal modes. Part II: Activation/orthogonality conditions for shallow structural systems', Int. J. Non-Linear Mech. 38 (2003) 873-887.
24. Cartmell, M.P., 'On the need for control of nonlinear oscillations in machine systems', MECCANICA Int. J. Ital. Assoc. Theo. Appl. Mech. 38(2) (2003) 185-212.
25. Nayfeh, A.H., Introduction to Perturbation Technique, Wiley, New York, 1981.