Modeling and investigation of a multi-resonant metamaterial sound insulator

A design of multi-resonant acoustic metamaterial sound insulator is proposed to attenuate multi-tonal and broadband noise. The unit cell of the metamaterial consists of a porous material with four, nine, and sixteen embedded Helmholtz resonators and its sound attenuation performance is studied using finite element method (FEM). A theoretical approach based on transfer matrix method is proposed and the theoretical results of the sound absorption and the transmission loss (TL) agree well with FEM results. Compared to the porous layer with one embedded resonator that presents one TL and one sound absorption resonant peak, the metamaterial made of four, nine, and sixteen embedded resonators exhibits respectively four, nine and sixteen sound absorption and TL resonant peaks. The sound absorption at various incidence angles and the diffuse field sound absorption of the proposed metamaterial are studied. At each resonant frequency, the acoustic pressure is maximum in the cavity of the corresponding resonator while in the associated neck, the acoustic velocity is maximum with important acoustic power dissipation density. As the incidence angle increases, the acoustic pressure in the cavity at the resonant frequencies decreases as well as the velocity in the necks and the power dissipation density becomes negligible, resulting in a decrease of the sound absorption. As the number of resonators within the porous layer increases, the sound absorption and TL frequency band enlarges. Compared to the conventional porous layer, the sound absorption and the TL are significantly improved at the resonant frequencies of the resonators.