Interactions Between Two Coupled Nonlinear Forced Systems: Fast/Slow Dynamics

Simon Charlemagne (1) , Alireza Ture Savadkoohi (1) , Claude-Henri Lamarque (1)

1 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes

Dynamics of a system formed by a linear structure coupled to a light nonlinear oscillator, both subjected to external excitations, is studied. Effects of the external forcing of the nonlinear oscillator are especially investigated. Complex geometry of the slow invariant manifold and equilibrium and singular points of the system are detected thanks to a multiple time scale strategy around 1:1:1 resonance. Equilibrium points lead to periodic regimes while singular points are hints of strongly modulated response of the system characterized by repeated bifurcations around its stable zones. A method for detection of changes in mechanical properties of main structural system is explained. Numerical simulations obtained by direct integration of the system are used to validate analytical predictions.

Mots clés: Fast/slow dynamics; nonlinear oscillators; passive control; energy transfer

Domaines: Science non linéaire [physics]; Sciences de l'ingénieur [physics]; Physique [physics]

Simon Charlemagne, Alireza Ture Savadkoohi, Claude-Henri Lamarque. Interactions Between Two Coupled Nonlinear Forced Systems: Fast/Slow Dynamics. International journal of bifurcation and chaos in applied sciences and engineering , 2016, 26 (9), 1650155 (28 p.). ⟨10.1142/S0218127416501558⟩. ⟨hal-01358576⟩