Complexity and Chaos of Parametrically and Self-Excited System with Non-Ideal Energy Source


Article Preview



Materials Science Forum (Volumes 440-441)

Edited by:

M.P. Cartmell




J. Warminski, "Complexity and Chaos of Parametrically and Self-Excited System with Non-Ideal Energy Source", Materials Science Forum, Vols. 440-441, pp. 363-370, 2003

Online since:

November 2003





[1] J. Warminski: Synchronisation Effects and Chaos in van der Pol-Mathieu Oscillator, Journal of Theoretical and Applied Mechanics, 2, 40, (2002), pp.415-433.

[2] A. Tondl, H. Ecker: Cancelling of Self-Excited Vibrations by Means of Parametric Excitation. Proceedings of the 1999 ASME Design Engineering Technical Conferences, DETC99/VIB-8071, Las Vegas, Nevada, USA, (1999).

[3] K. Szabelski, J. Warminski: The self-excited system vibrations with the parametric and external excitations, Journal of Sound and Vibration, 187(4), (1995), pp.595-607.


[4] K. Szabelski, J. Warminski: The parametric self excited non-linear system vibrations analysis with the inertial excitation, Int. Journal of Non-Linear Mechanics, Vol. 30, No 2, (1995), pp.179-189.


[5] V.O. Kononenko: Vibrating Systems with Limited Power Supply, (Illife, 1969).

[6] J. Warminski: Regular and Chaotic Vibrations of Parametrically and Self-Excited Systems with Ideal and Non-Ideal Energy Sources, (Technical University of Lublin Publisher, Lublin, Poland, 2001, monograph in Polish).

[7] J. Warminski, J.M. Balthazar, R.M.L.R.F. Brasil: Vibrations of Non-Ideal Parametrically and Self-Excited Model, Journal of Sound and Vibration, 245 (2), (2001), pp.363-374.


[8] W. Pełczy � ski, M. Krynke: Method of State Variables in Analysis of Power Transmission System Dynamics, (WNT, Warsaw, Poland, 1984, in Polish).

[9] N.N. Bogolubov, J.A. Mitropolsky: Asymptotic Methods in Non-linear Vibrations Theory, (Moscow, GIF-ML, 1958, in Russian).