Theory and experiments on poro-acoustics with inner resonators

• Analytical model describing meta-porous media in local and global dynamic.
• Direct assessment of the wide low frequency band gap.
• Inner resonance results in an apparent negative gas compressibility.
• Experiments on prototypes evidence high absorption and dispersion at low frequency.
• The validated theory provides practical rules for realizing tunable meta-materials.

The work proposed here deals with theory and experiment on the acoustics of gas saturated rigid porous media with inner resonance effects. First, we investigate the physics of porous media in which inner resonance phenomena occur. Then, through the homogenization method the macroscopic descriptions of (i) porous media constituted by a packing of Helmholtz resonators and of (ii) Helmholtz resonators embedded in a porous matrix are established. Around the eigen frequency of the resonator, the drastic change in the behavior of the medium results in band-gaps that can be determined analytically. Second, following the physical principles governing the inner resonance, several prototypes of such media are designed. Moreover, several extensions of this basic principle are described analytically and tested experimentally. Specific features of porous media embedding inner resonance effects are identified by common acoustic measurements and are shown to be in good agreement with the theory. Among the noteworthy results shown, it is confirmed experimentally that the resonators essentially modify the effective bulk modulus of the medium inducing strong velocity dispersion and high attenuation in the frequency range of the theoretical band gaps. In conclusion, we discuss the forthcoming applications of the macroscopic modeling, especially as a tool for designing new materials with unconventional properties such as large dissipation at low frequencies.