Nonlinear Dynamics

, Volume 52, Issue 4, pp 367–376 | Cite as

Nonlinear normal modes in homogeneous system with time delays

  • O. V. Gendelman
Original Paper


Periodic synchronous regimes of motion are investigated in symmetric homogeneous system of coupled essentially nonlinear oscillators with time delays. Such regimes are similar to nonlinear normal modes (NNMs), known for corresponding conservative system without delays, and can be found analytically. Unlikely the conservative counterpart, the system possesses “oval” modes with constant phase shift between the oscillators, in addition to symmetric/antisymmetric and localized regimes of motion. Numeric simulation demonstrates that the “oval” modes may be attractors of the phase flow. These attractors are particular case of phase-locked solutions, rather ubiquitous in the system under investigation.


Nonlinear normal modes Time-delay systems 


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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringTechnion—Israel Institute of TechnologyHaifaIsrael

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