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4 results on '"homogenized boundary conditions"'

1. A stable, unified model for resonant Faraday cages.

Author

Delourme, B., Lunéville, E., Marigo, J.-J., Maurel, A., Mercier, J.-F., and Pham, K.

Subjects
*ACOUSTIC arrays, *THEORY of wave motion, *RESONANCE, *DISTANCES
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. A472, 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. A472, 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. [ABSTRACT FROM AUTHOR]

Published
2021
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2. Homogenized boundary conditions and resonance effects in Faraday cages.

Author

Hewett, D. P. and Hewitt, I. J.

Subjects
*FARADAY cage, *RESONANCE effect, *ELECTROMAGNETIC shielding, *BOUNDARY value problems, *SOUND wave scattering
Abstract

We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called 'Faraday cage effect'). Taking the limit as the number of wires in the cage tends to infinity, we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarization of the incident field. In the electromagnetic case, there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model, we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells. [ABSTRACT FROM AUTHOR]

Published
2016
Full Text
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3. A stable, unified model for resonant Faraday cages

Author

Jean-Jacques Marigo, Eric Lunéville, Agnès Maurel, Jean-François Mercier, Kim Pham, Bérangère Delourme, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Propagation des Ondes : Étude Mathématique et Simulation (POEMS), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Institut Laue-Langevin (ILL), ILL, École Nationale Supérieure de Techniques Avancées (ENSTA Paris), Institut des Sciences de la mécanique et Applications industrielles (IMSIA - UMR 9219), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), École polytechnique (X)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-EDF R&D (EDF R&D), Institut Langevin, ESPCI Paris - PSL (IL), and ENSTA, IMSIA, Institut Polytechnique de Paris

Subjects
Asymptotic analysis, Wave propagation, General Mathematics, General Physics and Astronomy, 02 engineering and technology, 01 natural sciences, Dirichlet distribution, 010305 fluids & plasmas, law.invention, mathematical physics, symbols.namesake, 0203 mechanical engineering, law, 0103 physical sciences, [SPI.NANO]Engineering Sciences [physics]/Micro and nanotechnologies/Microelectronics, Faraday cage, [PHYS]Physics [physics], Physics, homogenized boundary conditions, [SPI.ACOU]Engineering Sciences [physics]/Acoustics [physics.class-ph], General Engineering, thin periodic interface, Unified Model, high order homogenization, Computational physics, 020303 mechanical engineering & transports, Transmission (telecommunications), symbols, waves asymptotic analysis, Research Article
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.

Published
2021

4. Homogenized boundary conditions and resonance effects in Faraday cages

Author

Ian Hewitt and David P. Hewett

Subjects
Wave propagation, General Mathematics, General Physics and Astronomy, FOS: Physical sciences, 01 natural sciences, Corrections, 010305 fluids & plasmas, law.invention, electromagnetic shielding, 78A40, 31A25, 78M40, Mathematics - Analysis of PDEs, law, 0103 physical sciences, FOS: Mathematics, Physics::Atomic and Molecular Clusters, Helmholtz equation, Boundary value problem, 010306 general physics, Faraday cage, Research Articles, Mathematical Physics, Multiple-scale analysis, homogenized boundary conditions, Physics, Scattering, General Engineering, thin periodic interface, Resonance, Mechanics, Mathematical Physics (math-ph), multiple scattering, Electromagnetic shielding, method of multiple scales, Microwave, Analysis of PDEs (math.AP)
Abstract

We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called `Faraday cage effect'). Taking the limit as the number of wires in the cage tends to infinity we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarisation of the incident field. In the electromagnetic case there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells., Comment: This revised version corrects some errors present in the journal published version

Published
2016

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