Juliette Pierre (MPIA)

Materials with elastic membranes : negative acoustic density 

Juliette Pierre¹,Valentin Leroy² and Benjamin Dollet^3
1 : Institut ∂’Alembert, Sorbonne Université, CNRS, 75005 Paris, France
² : MSC, University Paris Cité, CNRS, 75013Paris, France
³ : LIPhy, University Grenoble Alpes, CNRS, 38000 Grenoble, France
Cette adresse e-mail est protégée contre les robots spammeurs. Vous devez activer le JavaScript pour la visualiser.

Metamaterials are structured materials that exhibit unique wave-propagation behaviors arising from their microstructure. Among the most frequently discussed exotic properties of metamaterials are negative constitutive parameters, such as negative permeability and/or permittivity in electromagnetism, and negative density and/or compressibility in acoustics.

The concept of  « negative density » often appears the most difficult to accept at first sight, since it is hard to imagine a negative gravitational density. In acoustics, however, this notion refers to inertial density, which can indeed take negative values without conceptual difficulty. In a recent theoretical study, we introduced a simple system to illustrate the emergence of negative density, where an elastic response can be interpreted as an inertial response [1]. This system provides analytical expressions and serves as a simplified model that qualitatively reproduces the acoustic behavior observed in several existing membrane-based metamaterials [2–4].

[1] Pierre J, Leroy V, Dollet B. 2022 A toy model for the effective density of acoustic metamaterials. Proc. R. Soc. A 478: 20210861. 

[2] Pierre J, Dollet B, Leroy V. 2014 Resonant acoustic propagation and negative density in liquid foams. Phys. Rev. Lett. 112, 148307. 

[3] Ma G, Sheng P. 2016 Acoustic metamaterials: from local resonances to broad horizons. Sci. Adv. 2, e1501595 

[4] Malléjac M, Merkel A, Sanchez-Dehesa J, Christensen J, Tournat V, Groby JP, Romero-García V. 2019 Zero-phase propagation in realistic plate- type acoustic metamaterials. Appl. Phys. Lett. 115, 134101 

[5] Lee SH, Park CM, Seo YM, Wang ZG, Kim CK. 2009 Acoustic metamaterial with negative density. Phys. Lett. A 373, 4464–4469.