A stable, unified model for resonant Faraday cages

Author:

Delourme B.1,Lunéville E.2,Marigo J.-J.3,Maurel A.4ORCID,Mercier J.-F.2,Pham K.5ORCID

Affiliation:

1. LAGA, Université Paris 13, Villetaneuse, France

2. Poems, CNRS, ENSTA ParisTech, INRIA, 828 Bd des Maréchaux, 91762 Palaiseau, France

3. LMS, CNRS, Ecole Polytechnique, 91120 Palaiseau, France

4. Institut Langevin, CNRS, ESPCI ParisTech, 1 rue Jussieu, 75005 Paris, France

5. IMSIA, CNRS, ENSTA ParisTech, 828 Bd des Maréchaux, 91732 Palaiseau, France

Abstract

We study some effective transmission conditions able to reproduce the effect of a periodic array of Dirichlet wires on wave propagation, in particular when the array delimits an acoustic Faraday cage able to resonate. In the study of Hewett & Hewitt (2016 Proc. R. Soc. A 472 , 20160062 ( doi:10.1098/rspa.2016.0062 )) different transmission conditions emerge from the asymptotic analysis whose validity depends on the frequency, specifically the distance to a resonance frequency of the cage. In practice, dealing with such conditions is difficult, especially if the problem is set in the time domain. In the present study, we demonstrate the validity of a simpler unified model derived in Marigo & Maurel (2016 Proc. R. Soc. A 472 , 20160068 ( doi:10.1098/rspa.2016.0068 )), where unified means valid whatever the distance to the resonance frequencies. The effectiveness of the model is discussed in the harmonic regime owing to explicit solutions. It is also exemplified in the time domain, where a formulation guaranteeing the stability of the numerical scheme has been implemented.

Funder

AID/DGA

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

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