Period-doubling bifurcation tracking for the Harmonic Balance Method: application to a Duffing oscillator with asymmetric clearances

Roberto Alcorta , Benoit Prabel (1) , Sébastien Baguet (2) , Georges Jacquet-Richardet (2)

1 DYN - Laboratoire d'études de DYNamique
2 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]

This works presents a contribution to numerical bifurcation analysis of nonlinear vibrations via techniques based on the Harmonic Balance Method (HBM) and pseudo-arclength continuation. In particular, an original procedure for the detection, computation and tracking of period-doubling bifurcations-as well as branch switching-within said formalism is proposed. This approach is then used to explore the effects of asymmetry in a simple piecewise-continuous test case, where it successfully predicted phenomena such as 2T-periodic isola formation and subharmonic-response branches.

Domaines: Vibrations [physics.class-ph]

Roberto Alcorta, Benoit Prabel, Sébastien Baguet, Georges Jacquet-Richardet. Period-doubling bifurcation tracking for the Harmonic Balance Method: application to a Duffing oscillator with asymmetric clearances. NODYCON 2019 First International Nonlinear Dynamics Conference, Feb 2019, Rome, Italy. ⟨hal-02365970⟩