Abstract:

The acoustic wave propagation in gas-saturated double-porosity materials composed of a microporous matrix and mesopores with arrays of plate-type resonators is investigated. A macroscopic description, established with the two-scale asymptotic homogenization method, evidences the combined effect of inner resonances on the acoustic properties of the respective effective visco-thermal fluid. One type of resonance originates from strong pore-scale fluid-structure interaction, while the other one arises from pressure diffusion. These phenomena respectively cause weakly and highly damped resonances, which are activated by internal momentum or mass sources, and can largely influence, depending on the material’s morphology, either the effective fluid’s dynamic density, compressibility, or both. We introduce semi-analytical models to illustrate the key effective properties of the studied multiscale metamaterials. The results provide insights for the bottom-up design of multiscale acoustic metamaterials with exotic behaviors, such as the negative, very slow, or supersonic phase velocity, as well as sub-wavelength bandgaps.

Key words: wave propagation, homogenization, multiscale, metamaterial, permeo-elasticity, double-porosity material