Homogenization of sound-absorbing and high-contrast acoustic metamaterials in subcritical regimes
Abstract
We propose a quantitative effective medium theory for two types of acoustic
metamaterials constituted of a large number $N$ of small heterogeneities of
characteristic size $s$, randomly and independently distributed in a bounded
domain. We first consider a ``sound-absorbing'' material, in which the total
wave field satisfies a Dirichlet boundary condition on the acoustic obstacles. In
the ``sub-critical'' regime $sN=O(1)$, we obtain that the effective medium is
governed by a dissipative Lippmann-Schwinger equation which approximates the
total field with a relative mean-square error of order
$O(\max((sN)^{2}N^{-\frac{1}{3}}, N^{-\frac{1}{2}}))$. We retrieve the critical
size $s\sim 1/N$ of the literature at which the effects of the obstacles can be
modelled by a ``strange term'' added to the Helmholtz equation. Second, we
consider high-contrast acoustic metamaterials, in which each of the $N$
heterogeneities are packets of $K$ inclusions filled with a material of density
much lower than the one of the background medium. As the contrast parameter
vanishes, $\delta\rightarrow 0$, the effective medium admits $K$ resonant
characteristic sizes $(s_i(\delta))_{1\
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Florian Feppon : Connect in order to contact the contributor
https://hal.science/hal-03372593
Submitted on : Sunday, October 10, 2021-9:38:17 PM
Last modification on : Saturday, October 16, 2021-3:10:25 AM
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- HAL Id : hal-03372593 , version 1
Cite
F Feppon, H Ammari. Homogenization of sound-absorbing and high-contrast acoustic metamaterials in subcritical regimes. 2021. ⟨hal-03372593⟩
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