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Abstract:
Acoustic wave propagation in porous composites is investigated in this paper. The two-scale asymptotic homogenisation method is used to obtain the macroscopic description of sound propagation in such composites. The developed theory is both exemplified by introducing analytical models for the effective acoustical properties of porous composites with canonical inclusion patterns (i.e. a porous matrix with a periodic array of cylindrical or spherical inclusions) and validated by comparing the models predictions with the results of direct finite-element simulations and experimental testing, showing good agreement in all cases. It is concluded that the developed theory correctly captures the acoustic interaction between the constituents of the porous composite and elucidates the physical mechanisms underlying the dissipation of sound energy in such composites. These correspond to classical visco-thermal dissipation in the porous constituents, together with, for the case of composites made from constituents characterised by highly contrasted permeabilities, pressure diffusion which provides additional and tunable sound energy dissipation. In addition, this work determines the conditions for which a rigidly-backed porous composite layer can present improved sound absorption performance in comparison with that of layers made from their individual constituents. Hence, the presented results are expected to guide the rational design of porous composites with superior acoustic performance.

Keywords:
porous composites, wave propagation, acoustical properties, homogenisation, pressure diffusion

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.

Abstract:
Sound absorption of polydisperse heterogeneous porous composites is investigated in this paper. The wave equation in polydisperse heterogeneous porous composites is upscaled by using the two-scale method of homogenisation, which allows the material to be modeled as an equivalent fluid with atypical effective parameters. This upscaled model is numerically validated and demonstrates that the dissipation of sound in polydisperse heterogeneous porous composites is due to visco-thermal dissipation in the composite constituents and multiple pressure diffusion in the polydisperse heterogeneous inclusions. Analytical and semi-analytical models are developed for the acoustical effective parameters of polydisperse heterogeneous porous composites with canonical geometry (e.g. porous matrix with cylindrical and spherical inclusions) and with complex geometries. Furthermore, by comparing the sound absorption coefficient of a hard-backed composite layer with that of layers made from the composite constituents alone, it is demonstrated that embedding polydisperse heterogeneous inclusions in a porous matrix can provide a practical way for significantly increasing low frequency sound absorption. The results of this work are expected to serve as a model for the rational design of novel acoustic materials with enhanced sound absorption properties.