Enhancing Sound Attenuation in Permeable Heterogeneous Materials via Diffusion Processes

Abstract

This paper illustrates the concept of inducing multiple local non-equilibrium pressure states in permeable rigid frame materials by means of introducing specific geometrical patterns or material heterogeneities locally. This results in enhanced sound attenuation that is mostly determined by the local non-equilibrium pressure states of diffusive type. We illustrate the results by introducing analytical models for the long-wavelength acoustical properties of i) a perforated porous matrix with concentric annular and cylindrical porous inclusions co-axially inserted in the perforations, and ii) a heterogeneous array of highly resistive porous cylinders. The models predictions are compared with numerical simulations showing good agreement.