Application of the homogenization method in modelling and optimization of acoustic wave propagation on periodic perforated layers

The lecture will introduce several applications of the homogenization method based on the asymptotic analysis of periodically heterogeneous structures. These include modelling of piezoelectric materials, of elastic waves in composites with large contrasts in elastic modulae, giving rise to band gaps preservation in the homogenized limit, and the homogenization of acoustic waves in periodically perforated layers.

In the last case the essential steps of the analysis will be explained in more detail; the homogenized model supplies the transmission condition which is involved in acoustic problems in domains with sieves. Using numerical examples it will be illustrated how a suitable design of the perforation microstructure can modify the overall acoustic response viewed e.g. in terms of transmission losses. Also the sensitivity analysis of the macroscopic response w.r.t. design changes in the perforation will be mentioned. In the conclusion, an overview of possible applications and adaptations of the modelling approach in problems of optics and electromagnetic waves propagation is suggested.