Abstract

This paper investigates acoustic wave propagation in gas-saturated permeable lossy metamaterials, which have different types of resonators, namely, acoustic and elastic resonators, as building-block elements. By using the two-scale asymptotic homogenization method, the macroscopic equations that govern sound propagation in such metamaterials are established. These equations show that the metamaterials can be modeled as equivalent fluids with unconventional effective density and compressibility. Analysis of these frequency-dependent and complex-valued parameters shows that the real parts of both can take negative values within frequency bands determined by inner resonances. The upscaled theory is exemplified with the case of a permeable lossy metamaterial having a unit cell comprising two unconnected fluid networks and a solid frame. One of these fluid networks is loaded with acoustic resonators (e.g., quarter-wavelength, Helmholtz resonators), while thin elastic films are present in the other one. It is shown that the propagation of acoustic waves in permeable lossy metamaterials is determined by both classical visco-thermal dissipation and local elasto-inertial resonances. The results are expected to lead to judicious designs of acoustic materials with peculiar properties including negative phase velocity and phase constant characteristic for regressive waves, very slow phase velocity, and wide sub-wavelength bandgaps.