Effect of Variability in Micro-geometry of Polyurethane Foams on the Double Wall Transmission Loss

Propagation of waves in elastic porous media, e.g. polymeric foams, is described by Biot-Allard’s theory [1]. Two classes of characteristic parameters are needed to describe the porous media in this theory. First, non-acoustic parameters: porosity φ, thermal characteristic length Λ′, viscous characteristic length Λ, flow resistivity σ, and tortuosity α∞ which are used in Johnson-Champoux-Allard (JCA) semi-phenomenological model [1]. Second, mechanical parameters, which in the case of isotropic material, are: bulk density ρ, Young’s modulus E, loss factor η, and Poisson coefficient ν. The mechanical and non-acoustical properties are inherently dependent on the micro-structure of these materials. But, the internal structure of most porous material, e.g. polyurethane (PU) foam, is too complicated to be studied quantitatively. Therefore, the lattice of PU foams with low relative density (ρr) is commonly idealized by a tetrakaidecahedral, periodic unit cell (called PUC) and the macroscopic behavior recovered from a dedicated micro-macro approach. Furthermore, the cell windows can be randomly or partially closed, and cells are elongated in the rise direction. Measurements of such lattice results in variability in micro-structure properties of PUC. Hence, a clear understanding of the impact of variability associated with micro-structure properties measurement, and macroscopic Biot’s parameters on vibro-acoustical performance of PU foams is of great importance in the design and optimization of such foams. The impact of microstructure variability on JCA nonacoustical parameters and sound absorption was investigated by Doutres et. al [2]. This paper build on this work by investigating (i) the effect of the microstructure variability on the elastic properties of the foams and (ii) on the transmission loss of the foam when coupled with an elastic system (a double wall system is studied here). In this regard, a global sensitivity analysis (the FAST method) is applied to the micro-macro based models presented by Doutres et. al [3] and Gholami et. al [4]. The former model links the microstructure properties of PUC (thickness and length of struts, and the closed windows content) of polyurethane foams to their non-acoustical parameters of JCA model. While, the latter model correlates the micro-structure properties and membrane thickness of PU foam to the Young’s modulus in BiotAllard’s model.