Non-locality of the Willis coupling in fluid laminates

Matthieu Malléjac (1) , Théo Cavalieri (1) , Vicente Romero-García (1) , Aurélien Merkel , Daniel Torrent , Johan Christensen , Jensen Li , Jean-Philippe Groby (1)

1 LAUM - Laboratoire d'Acoustique de l'Université du Mans

The closed form expressions of the effective properties in periodic fluid laminates are derived thanks to the Padé approximation of the transfer matrix. A secondorder 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

Mots clés: Willis coupling; Non-locality; Laminate structures

Domaines: Acoustique [physics.class-ph]

Matthieu Malléjac, Théo Cavalieri, Vicente Romero-García, Aurélien Merkel, Daniel Torrent, et al.. Non-locality of the Willis coupling in fluid laminates. Wave Motion, 2022, 110, pp.102892. ⟨10.1016/j.wavemoti.2022.102892⟩. ⟨hal-03868360⟩