Effective acoustic properties of a meta-material consisting of small Helmholtz resonators

2016/03/17 by Lamacz, Agnes, Schweizer, Ben
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1603.05395

Abstract

We investigate the acoustic properties of meta-materials that are inspired by sound-absorbing structures. We show that it is possible to construct meta-materials with frequency-dependent effective properties, with large and/or negative permittivities. Mathematically, we investigate solutions u^ε: Ω_ε → ℝ to a Helmholtz equation in the limit ε→ 0 with the help of two-scale convergence. The domain Ω_ε is obtained by removing from an open set Ω⊂ ℝⁿ in a periodic fashion a large number (order ε^-n) of small resonators (order ε). The special properties of the meta-material are obtained through sub-scale structures in the perforations.

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