Acoustics modelling of open-cell foam materials from microstructure and constitutive properties

The dynamic relations for highly porous fibrous materials, having analytical expressions for dynamic viscous drag forces and oscillatory solid-to-fluid heat transfer, are now extended towards open-cell foam materials where the struts of the foam are considered to be primarily cylindrical except in the region of the joints. By also including analytical expressions for the stiffness of the foam cell, an entirely analytically-based model is presented for the acoustics of highly-porous, open-celled foam materials. This approach is extremely efficient, requiring only the mean cell size, mean strut diameter, and constitutive properties of the solid foam material and the surrounding viscous fluid as input. The acoustic performance prediction of not only isotropic foam cell designs, but also anisotropic ones may be performed rapidly and virtually, without the need for the determination of poroelastic material properties from existing material samples. The steps required for the development of the analytical foam-cell model are presented, along with the acoustic performance prediction of a typical Melamine foam cell, yielding very promising results in comparison against measurements. In order to understand the suitability of the cylindrical foam strut assumption, a viscous drag force comparison with foam struts having square and triangular cross-sectional profiles is also presented.