Vibratory control of a linear system by addition of a chain of nonlinear oscillators
Résumé
A N-degree-of-freedom model consisting of a single-degree-of-freedom linear system coupled
to a chain of (N − 1) light nonlinear oscillators is studied. The connection between the chain and the
single-degree-of-freedom system is supposed to be linear. Time multi-scale system behaviors at fast
and slow time scales are investigated and lead to detection of the Slow Invariant Manifold (SIM) and
equilibrium and singular points. These points correspond to periodic regimes and strongly modulated
responses, respectively. These analytical developments are used to provide evidence of transfer of vibratory
energy of the main system to the chain in the form of localized modes during periodic regimes and
extreme energy exchanges between modes when the overall structure faces singularities. Furthermore,
analytical predictions at slow time scale and nonlinear normal modes of the system are compared with
numerical results obtained from direct time integration of system equations, showing a good agreement
between them. Finally, we present a procedure showing how these analytical developments can be used
to study a system where the main structure is replaced by a multi-degree-of-freedom linear system, by
projecting its dynamics on one of its modes.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...