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Article Dans Une Revue SIAM Journal on Applied Mathematics Année : 2017

A mathematical and numerical framework for bubble meta-screens

David Gontier
Habib Ammari
Hyundae Lee
  • Fonction : Auteur
Hai Zhang
  • Fonction : Auteur

Résumé

The aim of this paper is to provide a mathematical and numerical framework for the analysis and design of bubble meta-screens. An acoustic meta-screen is a thin sheet with patterned subwavelength structures, which nevertheless has a macroscopic effect on the acoustic wave propagation. In this paper, periodic subwavelength bubbles mounted on a reflective surface (with Dirichlet boundary condition) is considered. It is shown that the structure behaves as an equivalent surface with Neumann boundary condition at the Minnaert resonant frequency which corresponds to a wavelength much greater than the size of the bubbles. Analytical formula for this resonance is derived. Numerical simulations confirm its accuracy and show how it depends on the ratio between the periodicity of the lattice, the size of the bubble, and the distance from the reflective surface. The results of this paper formally explain the super-absorption behavior observed in [V. Leroy et al., Phys. Rev. B, 2015].

Dates et versions

hal-01615041 , version 1 (11-10-2017)

Identifiants

Citer

David Gontier, Habib Ammari, Brian Fitzpatrick, Hyundae Lee, Hai Zhang. A mathematical and numerical framework for bubble meta-screens. SIAM Journal on Applied Mathematics, 2017, 77 (5), pp.1827--1850. ⟨10.1137/16M1090235⟩. ⟨hal-01615041⟩

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