Visco-thermal dissipations in heterogeneous porous media

Abstract

Semi-phenomenological models have been widely used since the 1990’s for modeling visco-thermal dissipations of acoustical energy through porous media. These dissipations are taken into account by two complex frequency-dependent functions (the dynamic density ρeq (ω) and the dynamic bulk modulus Keq (ω)), which are analytically derived from macroscopic parameters. Other models were derived for modeling perforated plates [J. Sound Vib. 303 (2007)], double porosity media [J. Acoust. Soc. Am. 114(1) (2003)] or, more recently, porous composites made of porous inclusions in a substrate porous media [Acta Acoust. 96 (2010)]. So far, this latter model is not able to consider the shape of the host and the client media. This model can neither be extended to limiting cases of perforated plate model nor double porosity model. Based on a modified equivalent fluid model, this work proposes a unified model which accounts, analytically, for the shape of the inclusions, might they be porous or not. This model enables to describe the acoustic behavior of any kind of composite media from perforated plates to arbitrarily shaped porous composites including configurations of porous inclusions in solid matrix or double porosity media. In addition, possible pressure interactions between the substrate material and the inclusions are accounted for.