Analytical and experimental study of a Vibro-Imapact Nonlinear Energy Sink
Résumé
This paper reports on the experimental and analytical study of a mechanical system coupled to a Vibro-Impact Nonlinear Energy Sink (VI-NES). The dynamics of such a system is experimentally investigated by carrying out several tests on a prototype harmonically forced, in order to analyse the VI-NES capability to absorb vibratory energy. The experimental setup is constituted by a primary single-degree-of-freedom linear oscillator (LO) to which a VI-NES is attached. The system’s response strongly depends on the external force. Two different kinds of steady (periodic) states are observed: a strongly modulated response and a constant amplitude response. In both cases an irreversible transfer of energy occurs from the LO towards the VI-NES; this process is referred to as passive targeted energy transfer (TET). Furthermore, the mathematical problem is analytically studied by using the multiple scales technique: it is shown that an energy threshold exists for steady solutions to be established and for TET to be captured into 1:1 resonance between the VI-NES and the LO. The energy threshold for the VI-NES activation is mathematically proved and correlated with the experimental tests. In the case of a damped and forced LO, the dependence of the activation threshold on external forcing is analytically demonstrated. The analytical solution defined the slow invariant manifold of the problem with respect to the fast time scale: it shows the existence of two branches of steady-state responses corresponding to stable and unstable solutions. These two kinds of solution are the mathematical counterpart of the strongly-modulated and constant-amplitude responses experimentally observed.