Membranes in the 3d Cellular Solid Model Provide the Micro-/macro Scaling for the Long-wavelength Acoustics of Real Foam Samples

The general objective of our work is the optimization of the long-wavelength acoustic properties of real sound proofing foam samples. In this purpose, our general methodology is to use the method of periodic unit cell (PUC) reconstruction of porous media which consists of two main steps. In the first one, the critical local geometry features governing long-wavelengths acoustic wave propagation and dissipation phenomena through porous media are identified. Then, one generates three-dimensional (3D) parameterized PUC suitable for optimization purposes, in which macroscopic properties are obtained by integrating the relevant partial differential equations. This short paper presents recent developments in the field of critical local characteristic sizes identification with application to real polymeric foam samples, where emphasis is put on the techniques which have been devised to account explicitly for the fundamental role played by membranes in the overall transport phenomena.