Resonance enhancement by suitably chosen frequency detuning

Denys Dutykh (1, 2, 3) , Elena Tobisch (4)

1 LAMA - Laboratoire de Mathématiques
2 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc
3 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
4 Institut für Analysis

In this Letter we report new effects of resonance detuning on various dynamical parameters of a generic 3-wave system. Namely, for suitably chosen values of detuning the variation range of amplitudes can be significantly wider than for exact resonance. Moreover, the range of energy variation is not symmetric with respect to the sign of the detuning. Finally, the period of the energy oscillation exhibits non-monotonic dependency on the magnitude of detuning. These results have important theoretical implications where nonlinear resonance analysis is involved, such as geophysics, plasma physics, fluid dynamics. Numerous practical applications are envisageable \eg in energy harvesting systems.

Mots clés: nonlinear resonance; frequency detuning; 3-wave system; resonance enhancement

Domaines: Mécanique des fluides [physics.class-ph]; Physique mathématique [math-ph]; Dynamique des Fluides [physics.flu-dyn]; Physique Atmosphérique et Océanique [physics.ao-ph]; Physique Classique [physics.class-ph]; Physique Numérique [physics.comp-ph]; Analyse numérique [math.NA]; Physique mathématique [math-ph]; Analyse classique [math.CA]; Systèmes Solubles et Intégrables [nlin.SI]

Denys Dutykh, Elena Tobisch. Resonance enhancement by suitably chosen frequency detuning. Mathematics , 2020, Turbulence Modeling, 8 (3), pp.450. ⟨10.3390/math8030450⟩. ⟨hal-01084796⟩