Finite element modeling of acoustic metamaterial based on periodic Helmholtz resonator with a membrane in the cavity

In this paper, a finite element design of acoustic metamaterial consisting of Helmholtz resonators periodically embedded into a porous material is proposed and studied numerically. The Helmholtz resonators contain a membrane in the cavity, and its contribution to the sound transmission loss (TL) improvement is investigated. The use of a membrane in the resonator cavity induces multiple resonances for the TL while only one resonant TL peak is observed when a conventional resonator is used. The theoretical and numerical results agree well. Finite element simulations are performed for free and fixed boundary conditions of the membrane inside the resonator cavity. The impacts of the thickness and the material properties of the membrane on the TL and on the eigenfrequencies of the membrane are analyzed. The TL presents multiple resonance peaks where certain resonance frequencies correspond to the eigenfrequencies of the membrane. The single and double wall configurations are studied numerically and the effects of the different parameters of the resonator and the membrane on the TL are presented. Numerical studies are performed to illustrate the sound attenuation mechanism and the effects of the airflow resistivity of the porous material as well as those of the incidence angles on the TL. The Helmholtz resonator design with a membrane in the cavity can be used in many engineering applications to attenuate multi-tonal noise at multiple frequencies simultaneously unlike a conventional resonator.