Nonlinear normal modes in homogeneous system with time delays
- 83 Downloads
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.
KeywordsNonlinear normal modes Time-delay systems
Unable to display preview. Download preview PDF.
- 1.Lyapunov, A.: The General Problem of the Stability of Motion. Princeton University Press, Princeton (1947) Google Scholar
- 6.Manevitch, L.I., Mikhlin, Yu.V., Pilipchuk, V.N.: The Method of Normal Vibrations for Essentially Nonlinear Systems. Nauka, Moscow (1989) (in Russian) Google Scholar
- 20.Morrison, T.M., Rand, R.H.: 2:1 Resonance in the delayed nonlinear Mathieu equation. Nonlinear Dyn. available online, doi: 10.1007/s11071-006-9162-5 (2007)