Equivalent fluid approach to modeling the acoustical properties of polydisperse heterogeneous porous composites

Abstract

This paper investigates sound propagation in polydisperse heterogeneous porous composites. The two-scale asymptotic method of homogenization is used to obtain a macroscopic description of the propagation of sound in such composites. The upscaled equations demonstrate that the studied composites can be modeled as equivalent fluids with complex-valued frequency-dependent effective parameters (i.e., dynamic viscous permeability and compressibility) as well as unravel the sound energy dissipation mechanisms involved. The upscaled theory is both exemplified by introducing analytical and hybrid models for the acoustical properties of porous composites with different geometries and constituent materials (e.g., a porous matrix with much less permeable and/or impervious inclusions with simple or complex shapes) and validated through computational experiments successfully. It is concluded that the developed theory rigorously captures the physics of acoustic wave propagation in polydisperse heterogeneous porous composites and shows that the mechanisms that contribute to the dissipation of sound energy in the composite are classical visco-thermal dissipation together with multiple pressure diffusion phenomena in the heterogeneous inclusions. The results show that the combination of two or more permeable materials with highly contrasted permeabilities can improve the acoustic absorption and transmission loss of the composite. This paper provides fundamental insights into the propagation of acoustic waves in complex composites that are expected to guide the rational design of novel acoustic materials.