Effective acoustic properties of a meta-material consisting of small Helmholtz resonators
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Date
2016-03-16
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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.
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Keywords
Helmholtz equation, homogenization, resonance, perforated domain, frequency dependent effective properties