Period doubling bifurcation analysis and isolated sub-harmonic resonances in an oscillator with asymmetric clearances

Roberto Alcorta , Sébastien Baguet (1) , Benoit Prabel (2) , Philippe Piteau (3) , Georges Jacquet-Richardet (4)

1 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
2 SEMT - Service d'Etudes Mécaniques et Thermiques
3 CEA-DES (ex-DEN) - CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire)
4 DCS - Dynamique et Contrôle des Structures

In this paper, a frequency-domain characterisation of the period-doubling bifurcation is proposed. This allows an efficient detection and localisation of such points along frequency-response curves computed through continuation and the harmonic balance method. A simple strategy for branch switching to sub-harmonic regimes is presented as well. Furthermore, these bifurcations are tracked in a two-dimensional parameter space, and extremum points with respect to the tracking parameter are characterized and linked to sub-harmonic isola formation. As a test case for these methods, a forced Duffing oscillator with asymmetric clearances is studied numerically. The results, which include the prediction of period-doubling cascades and sub-harmonic isolas, are then compared to experimental results, yielding an excellent agreement.

Domaines: Vibrations [physics.class-ph]

Roberto Alcorta, Sébastien Baguet, Benoit Prabel, Philippe Piteau, Georges Jacquet-Richardet. Period doubling bifurcation analysis and isolated sub-harmonic resonances in an oscillator with asymmetric clearances. Nonlinear Dynamics, 2019, 98, pp.2939-2960. ⟨10.1007/s11071-019-05245-6⟩. ⟨hal-02295420⟩