On the bifurcations of a fluttering plate in confined axial flow
Résumé
The flutter of cantilevered beams in channel flow is a benchmark example of flow-induced vibrations and its fundamental behavior is found in numerous practical applications. Experiments have shown that such systems present a wide variety of complex nonlinear behavior. However, the plethora of previous studies is mostly concerned with linear stability analysis. In this work, we provide an initial impulse for a comprehensive nonlinear study of these systems through bifurcation analysis. We consider a one-dimensional problem, where a cantilevered beam is treated in a modal framework and the surrounding flow is modelled by bulk-flow equations. The system is discretized in space and time via Galerkin procedures (modal, Tau and harmonic balance methods) and the continuation of periodic solutions is pursued using the asymptotic numerical method. The nonlinear dynamics are explored with respect to various dimensionless parameters, clarifying a number of behavioral trends: sub-critical bifurcations and hysteresis loops, grazing boundaries (separation between limit cycles with and without intermittent beam-wall impacts), internal resonances, torus bifurcations and quasi-periodic oscillations, amongst others. Aside from providing novel insights into the physics of fluttering beams, is it hoped that the methods used in here can stimulate similar studies in the field of flow-induced vibrations.
Origine : Fichiers produits par l'(les) auteur(s)
Licence : CC BY - Paternité
Licence : CC BY - Paternité