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arXiv · 1603.05395

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

Agnes Lamacz·Ben Schweizer
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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 $u^\varepsilon: \Omega_\varepsilon \rightarrow \mathbb{R}$ to a Helmholtz equation in the limit $\varepsilon\rightarrow 0$ with the help of two-scale convergence. The domain $\Omega_\varepsilon$ is obtained by removing from an open set $\Omega\subset \mathbb{R}^n$ in a periodic fashion a large number (order $\varepsilon^{-n}$) of small resonators (order $\varepsilon$). The special properties of the meta-material are obtained through sub-scale structures in the perforations.

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Agnes Lamacz, Ben Schweizer. 2016-03-17. Effective acoustic properties of a meta-material consisting of small Helmholtz resonators. https://arxiv.org/abs/1603.05395

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