Static airflow resistivity association law of a multilayer rigid porous material

Mono and multi-layer porous media are very often used in building engineering and aerospace industry to fight against noise pollution. These media are characterized by several acoustic parameters, the most important of which is the flow resistivity. In this article, a static airflow resistivity association law of multilayer rigid porous materials is proposed. The equivalent fluid theory is considered. The visco-inertial interactions between the structure and the pore-saturating fluid are taken into account by the dynamic tortuosity introduced by Johnson et al and the dynamic compressibility given by Allard. Simplified expressions of acoustic transmission coefficients of a monolayer and bilayer porous medium are established in the very low-frequency regime. The established expressions are independent of frequency and depend only on the airflow resistivity and the thickness of each layer. The equivalent flow resistivity of the bilayer medium is expressed as a function of the thickness and flow resistivity of each layer. The established law has been generalized to the case of a multilayer medium consisting of several different rigid porous layers. Experimental validation of the established law is carried out using a combination of several samples of polyurethane foams (PU) with different thicknesses and flow resistivity.