Numerical characterization of inclusion based acoustic meta-materials

Heterogeneous porous materials are widely used in building and transportation sectors. The heterogeneities arise due to recycling processes or are designed to include non-conventional phenomena (pressure diffusion, acoustic resonances, multiple-scattering, Bragg-interferences, sorption, etc.) involved in acoustical metamaterials. Detailed Finite Element Models (FEM) of such materials prove prohibitively expensive, especially when embedded in large structures. Although heterogeneous analytical methods address this issue, they exist only for specific, idealized scenarios; consequently a more robust generalization is achieved by generating a condensed transfer matrix (TMM) from a single unit cell FEM computation. The coupled TMM-FEM approach is further augmented by incorporating periodicity. However, the condensed TMM is useful but dependent on the excitation incident angle, i.e., it must be recomputed for each incidence. This work combines the condensed-TMM approach with a numerical characterization of equivalent intrinsic parameters. These equivalent parameters enable to analyse the involved physical phenomena at the macroscopic scale and to condense such heterogeneous material as a single layer in more complex structures. It is further showed, when dealing with FEM, that the proposed condensation has a high computational gain over the conventional full three-dimensional finite element approach, especially when dealing with excitations like diffuse field excitation. The accuracy and efficiency of the method, along with relevant examples will be discussed.