Theoretical and numerical study of targeted energy transfer inside an acoustic cavity by a non-linear membrane absorber

This paper investigates the Targeted Energy Transfer (TET) between an acoustic medium inside a parallelepiped cavity and a thin viscoelastic membrane that is mounted on one wall of the cavity and that is working as a Non-linear Energy Sink (NES). Applying a harmonic source excitation inside the cavity, we look for reducing the resonance peaks of the acoustic cavity by mean of the so-called “Strongly Modulated Response” (SMR). Using a single term harmonic balance approach, we determine analytical simplified expressions for the non-linear normal modes (NNMs) and the periodic forced responses of this coupled system. We define the “desired working zone” for the NES as the forcing level interval between the first destabilization of the resonance peak (TET beginning) and the appearance of an additional branch of periodic regimes. An analytical formula is derived for the beginning of TET while the appearance of the undesired periodic regimes is obtained numerically. These results prove to be useful for the practical design of NES to be mounted on an acoustic cavity.