, Volume 40, Issue 2, pp 181–202 | Cite as

Regular and Chaotic Vibrations of a Parametrically and Self-Excited System Under Internal Resonance Condition



Vibrations of a parametrically and self-excited system with two degrees of freedom have been analysed in this paper. The system is constituted by two parametrically coupled oscillators characterised by self-excitation and nonlinear Duffing’s type nonlinearities. Synchronisation phenomenon has been determined near the principal resonances in the neighbourhood of the first p1 and the second p2 natural frequencies, and near the combination resonance (p1+p2)/2. Vibrations have been investigated for parameters which satisfy the internal resonance condition p2/p1=3. The existence and break down of the synchronisation phenomenon have been revealed analytically by the multiple time scale method, whilst transition of the system to chaotic motion has been carried out numerically.


Self-excitation Parametric vibrations Synchronisation Internal resonance Chaos 


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© Springer 2005

Authors and Affiliations

  1. 1.Department of Applied MechanicsLublin University of TechnologyLublinPoland

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