RT Journal Article
T1 Non-locality of the Willis coupling in fluid laminates
A1 Malléjac, Matthieu
A1 Cavalieri, Théo
A1 Romero-García, Vicent
A1 Merkel, Aurélien
A1 Torrent, Daniel
A1 Christensen, Johan
A1 Li, Jensen
A1 Groby, Jean-Philippe
AB The closed form expressions of the effective properties in periodic fluid laminates are derived thanks to the Padé approximation of the transfer matrix. A second-order Taylor expansion of the transfer matrix elements exhibits Willis coupling. This coupling is the sum of a local term and a nonlocal term. The nonlocal term arises from the apparent bulk modulus in quasi one-dimensional problems. The nonlocality directly impacts the governing equations modeling the acoustic wave propagation in these Willis materials, which then involve convolution products in space. As an example, a two-orthotropic porous material laminate is considered. The theoretically derived effective properties and scattering coefficients are found in excellent agreement with those numerically calculated. The Willis coupling widens the frequency range of validity and accuracy of the effective properties and thus of the calculated scattering coefficients when compared to classical homogenization results for which the Willis coupling is absent. This widening mostly relies on the effect of Willis coupling on the impedance of the fluid laminate. The effective properties are finally derived for a general laminate.
PB Elsevier
SN 0165-2125
YR 2022
FD 2022-03
LK https://hdl.handle.net/10016/37417
UL https://hdl.handle.net/10016/37417
LA eng
NO J.-P.G., M.M., T.C. and V.R.-G. would like to acknowledge the support of the ANR-RGC METARoom project (ANR-18-CE08-0021). J.L. would like to acknowledge the support of the Research Grants Council in Hong Kong (Grant No. 16302218). D.T. acknowledges financial support through the "Ramón & Cajal" fellowship under grant number RYC-2016-21188.
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RD 27 jul. 2024