Summary
This work investigates the dynamic behavior of a Van der Pol oscillator (used as an archetypal self-sustained oscillator) coupled to a bistable nonlinear energy sink (BNES). First, numerical simulations show that this system can undergo a wide diversity of motions including different types of periodic regimes and so-called strongly modulated responses (SMR) as well as chaotic regimes. We also show that a BNES can be much more efficient than a classical cubic NES but a little perturbation can switch the system from harmless to harmful situations. However, even in the most unfavorable cases, a set of parameters can be found for which the BNES performs better than the NES. A fast-slow analysis of the amplitude-phase modulation dynamics (APMD) obtained by means of the so-called Multiple Scale/Harmonic Balance Method is then conducted within the framework of the geometric singular perturbation theory. A global stability analysis is partially performed from the computation of the so-called critical manifold and the APMD fixed points. This leads to interpret a certain number of regimes observed previously on numerical simulations of the initial full-order dynamics.
