Acoustic metamaterial containing an array of Helmholtz resonators coupled with mass-loaded membranes

Abstract

Acoustic metamaterial consisting of an array Helmholtz resonators has been revealed to have the band gap phenomenon which implies a great potential for noise reduction. However, the application of the conventional acoustic metamaterial is often limited by the narrow band gap. In this paper, an acoustic metamaterial containing a series of membrane-coupled Helmholtz resonators is proposed to produce mult iple band gaps in the low-frequency regime for achieving broadband noise reduction. First, a theoretical model is developed to describe the dynamic of the membrane-coupled Helmholtz resonator system. The membrane is assumed to be loaded with a small mass at the centre for tuning its natural frequencies, thus the resonances of the coupled system and the band gaps of the proposed acoustic metamaterial. Subsequently, based on the theory of acoustic wave propagation together with the derived theoretical model for the membrane-coupled Helmholtz resonator system, a theoretical analysis of the proposed acoustic metamaterial is performed. Using the Bloch’s theorem, the dispersion relation of the proposed acoustic metamaterial is derived. Multiple band gaps are observed in the band structure. A corresponding finite element model of the proposed metamaterial is built to confirm the predictions from the theoretical analysis.