|Title:||Effective acoustic properties of a meta-material consisting of small Helmholtz resonators|
|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 υ^ε:Ω^ε→ℝ to a Helmholtz equation in the limit ε→0 with the help of two-scale convergence. The domain Ωε 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.|
|Subject Headings:||Helmholtz equation|
frequency dependent effective properties
|Appears in Collections:||Preprints der Fakultät für Mathematik|
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