The targeted energy transfer (TET) phenomenon has been observed in the field of acoustics, which provides a new approach to passive sound control in low frequency domain. The TET phenomenon has been investigated firstly inside one tube (1D acoustic system) with a membrane nonlinear energy sink (NES) or a loudspeaker nonlinear absorber, then inside an acoustic cavity (3D acoustic system) with a membrane NES. 3D acoustic cavities have been considered as more general geometry for the acoustic medium in view of applications in the acoustic field and the membrane NES is mounted directly on the wall of the acoustic cavity. The placement of a membrane NES on the wall involves a weak coupling between the membrane NES and a considered acoustic mode, which constitute the two degrees-of-freedom (DOF) system. The beginning of TET phenomenon of the two DOFs system has been analyzed and the desired working zone for the membrane NES has also been defined. The two thresholds of the zone have been determined by an analytical formula and semi-analytically, respectively. The parametric analysis of the membrane NES by using the two DOFs system has been investigated to design the membrane NES. In order to enhance the robustness and the effective TET range in acoustic cavities, a three DOFs system with two membranes and one acoustic mode is studied in this paper. We consider two different membranes and two almost identical membranes to analyze the TET phenomenon, respectively. The desired working zone for the membrane NES and the value of the plateau which are obtained by the two DOFs system are applied to analyze the three DOFs system. We observe that two membranes can enlarge the desired working zone of the NES.

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