Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Homogenization of sound-absorbing and high-contrast acoustic metamaterials in subcritical regimes

by F. Feppon and H. Ammari

(Report number 2021-35)

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 \(ssim 1/N\) 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, \(deltarightarrow 0\), the effective medium admits \(K\) resonant characteristic sizes \((s_i(delta))_{1

Keywords: Non-periodic homogenization, effective medium theory, strange term, subwavelength resonance, high-contrast medium, holomorphic integral operators.

@Techreport{FA21_977,
  author = {F. Feppon and H. Ammari},
  title = {Homogenization of sound-absorbing and high-contrast acoustic metamaterials in subcritical regimes },
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2021-35},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2021/2021-35.pdf },
  year = {2021}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).