Multi-resonance capturing in a two-degree-of-freedom system under two different harmonic excitations

Abstract

In this paper we consider two coupled oscillators which exhibit energy transfer from master ‘linear’ degrees of freedom submitted to resonant external excitation with two different harmonics to a slave ‘nonlinear’ energy sink (NES). By endowing the idea of the relative mode, splitting harmonics and iterative techniques, we prove that control of the two one-to-one resonances of the system is possible simultaneously; moreover, the iterative technique gives us a better outlook over effects of the NES parameters on the overall behavior of the system. Then, analytical procedure for multi-resonance capture are explained and commented on. Finally, the obtained analytical results are compared with numerical evidence.