Algebraic model of a wall acoustic impedance constructed using experimental data

International audienceIn the context of a research devoted to the construction of a wall acoustic impedance model for a soundproofing scheme constituted of a porous medium inserted between two thin plates, an experimental data basis was carried out. In this paper, we present a probabilistic algebraic model of a wall acoustic impedance, constructed using this experimental data basis and allowing such a soundproofing scheme to be modeled. This kind of probabilistic algebraic model can be used for validating finite element model of such a soundproofing scheme whose equations are derived from the Biot theory, or for validating theoretical model, adapted to medium and high frequency ranges, deduced from Biot's equations. This probabilistic algebraic model is constructed by using the general mathematical properties of wall acoustic impedance operators (symmetry, odd and even functions with respect to the frequency, decreasing functions when frequency goes to infinity, behavior when frequency goes to zero and so on). The parameters introduced in this probabilistic algebraic model are fitted with the experimental data basis