On the modelling of membrane-coupled Helmholtz resonator and its application in acoustic metamaterial system

•Two SDOF (single-degree-of-freedom) models for representing the membrane have been proposed.•The transformation coefficients for describing the acoustic-mechanical coupling have been derived.•A MDOF model for representing the membrane coupled Helmholtz resonator has been developed.•An acoustic metamaterial integrated with membrane coupled Helmholtz resonator has been studied. In recent years, the Helmholtz resonator and membrane are two popular elements that have been vastly employed in the design of energy harvesters and metamaterials. In this paper, a theoretical study of the modelling of the membrane-coupled Helmholtz resonator is presented. The membrane is first represented with lumped parameters as a single-degree-of-freedom piston/centre-mass model. The physical meaning of the effective force-bearing area is explained. The membrane-coupled Helmholtz resonator is then modelled as a multiple-degree-of-freedom system. From the acoustic-mechanical interaction perspective, transformation coefficients are derived to bridge the acoustic and mechanical domains. Inspired by the fact that the membrane-coupled Helmholtz resonator exhibits multiple resonances in the low frequency regime, an acoustic metamaterial system is proposed by integrating the membrane-coupled Helmholtz resonators. A theoretical model of the proposed acoustic metamaterial is developed and multiple band gaps are predicted from the band structure analysis. All the theoretical models presented in this paper have been verified by corresponding finite element models.