Dynamics and energy exchanges between a linear oscillator and a nonlinear absorber with local and global potentials

The dynamical behavior of a two degree-of-freedom system made up of a linear oscillator and a coupled nonlinear energy sink with nonlinear global and local potentials is studied. The nonlinear global potential of the energy sink performs direct interactions with the linear oscillator, while its local potential depends only on its own behavior during vibratory energy exchanges between two oscillators. A time multiple scale method around 1:1:1 resonance is used to detect slow invariant manifold of the system, its equilibrium and singular points. Detected equilibrium points permit us to predict periodic regime(s) while singular points can lead the system to strongly modulated responses characterized by persistent bifurcations. Several possible scenarios occurring during these strongly modulated regimes are highlighted. All analytical predictions are compared with those which are obtained by direct numerical integration of system equations.