Modelling the effective sound propagation properties of a hexagonal acoustic metamaterial using a dissipative equivalent-fluid approach under different termination conditions

This paper presents a theoretical approach to assess the effective sound propagation properties of an acoustic system comprising multiple subwavelength resonators under grazing incidence. Consequently, the high capacity required to handle sound transmission, absorption and reflection are theoretically and experimentally reported. Viscothermal effects are considered by employing the dissipative equivalent-fluid approach and the respective analytical estimations of transport parameters provide accuracy in describing the resistive and reactive phenomena in the acoustic field for different termination conditions. The dissipative equivalent-fluid approach proposed here is contrasted with other well-established methods and numerical computing. The results evidence good agreement even when multiple resonances are associated, enabling the implementation of single, dual and triple resonance systems. The results of this work present a validated simplified approach that provides analytical derivations of the effective sound propagation properties in a complex association of side-branches Helmholtz resonators.