Abstract
Targeted energy transfer between a main oscillator with a set of parallel Saint-Venant elements and a nonlinear energy sink with a general nonlinear and odd potential function around 1:1 resonance is studied. The complexified system has been investigated at fast and slow time scales by detecting its invariant manifold, equilibrium and singular points, which can explain bifurcation(s) and different regimes of the system. Then, we introduce an example which treats vibratory energy exchanges between a main oscillator with two parallel Saint-Venant elements and a coupled cubic nonlinear energy sink. Finally, analytical predictions are compared with results obtained by numerical integrations of system equations.
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