Application of the transfer matrix approximation for wave propagation in a metafluid representing an acoustic black hole duct termination

The transfer matrix method has been proposed to analyze the acoustic black hole effect in duct terminations. The latter is achieved by placing a retarding waveguide structure inside the duct, which consists in a set of rings whose inner radii decrease to zero following a power law. The rings are sep...

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Detalles Bibliográficos
Autores: Guasch Fortuny, Oriol, Sánchez Martín, Patricia|||0000-0001-6937-0155, Ghilardi, Davide
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/419484
Acceso en línea:https://hdl.handle.net/2117/419484
https://dx.doi.org/10.1016/j.apm.2019.09.039
Access Level:acceso abierto
Palabra clave:Acoustic black hole
Metafluid
Transfer matrix method
Metamaterial
Waveguide power-law radius
Reflection coefficient
Àrees temàtiques de la UPC::Matemàtiques i estadística
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spelling Application of the transfer matrix approximation for wave propagation in a metafluid representing an acoustic black hole duct terminationGuasch Fortuny, OriolSánchez Martín, Patricia|||0000-0001-6937-0155Ghilardi, DavideAcoustic black holeMetafluidTransfer matrix methodMetamaterialWaveguide power-law radiusReflection coefficientÀrees temàtiques de la UPC::Matemàtiques i estadísticaThe transfer matrix method has been proposed to analyze the acoustic black hole effect in duct terminations. The latter is achieved by placing a retarding waveguide structure inside the duct, which consists in a set of rings whose inner radii decrease to zero following a power law. The rings are separated by thin air cavities. If the number of ring-cavity ensembles is large enough, wave propagation inside the waveguide can be treated as a continuous problem. A governing differential equation can be derived for the acoustic black hole which intrinsically relies on assumptions from transfer matrix theory. However, no formal demonstration exists showing that the transfer matrix solution is consistent and formally tends to the solution of the continuous problem. Proving such consistency is the main goal of the paper and an original option has been adopted to this purpose. First, we prove the differential equation for the acoustic black hole is identical to the wave equation for a metafluid with a power-law varying density. Transfer matrices are then applied to solve wave propagation in a discretization of the metafluid into layers of constant density. It is shown that when the number of layers tends to infinity and their thicknesses to zero, the transfer matrix solution satisfies the metafluid equation and therefore the acoustic black hole one. The transfer matrices for the metafluid discrete layers take a particularly simple form, which is a great advantage. This work allows one to interpret the retarding waveguide structure as a particular realization of the metafluid.20202020-01-0120242024-11-28journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/419484https://dx.doi.org/10.1016/j.apm.2019.09.039reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4194842026-05-27T15:37:01Z
dc.title.none.fl_str_mv Application of the transfer matrix approximation for wave propagation in a metafluid representing an acoustic black hole duct termination
title Application of the transfer matrix approximation for wave propagation in a metafluid representing an acoustic black hole duct termination
spellingShingle Application of the transfer matrix approximation for wave propagation in a metafluid representing an acoustic black hole duct termination
Guasch Fortuny, Oriol
Acoustic black hole
Metafluid
Transfer matrix method
Metamaterial
Waveguide power-law radius
Reflection coefficient
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short Application of the transfer matrix approximation for wave propagation in a metafluid representing an acoustic black hole duct termination
title_full Application of the transfer matrix approximation for wave propagation in a metafluid representing an acoustic black hole duct termination
title_fullStr Application of the transfer matrix approximation for wave propagation in a metafluid representing an acoustic black hole duct termination
title_full_unstemmed Application of the transfer matrix approximation for wave propagation in a metafluid representing an acoustic black hole duct termination
title_sort Application of the transfer matrix approximation for wave propagation in a metafluid representing an acoustic black hole duct termination
dc.creator.none.fl_str_mv Guasch Fortuny, Oriol
Sánchez Martín, Patricia|||0000-0001-6937-0155
Ghilardi, Davide
author Guasch Fortuny, Oriol
author_facet Guasch Fortuny, Oriol
Sánchez Martín, Patricia|||0000-0001-6937-0155
Ghilardi, Davide
author_role author
author2 Sánchez Martín, Patricia|||0000-0001-6937-0155
Ghilardi, Davide
author2_role author
author
dc.subject.none.fl_str_mv Acoustic black hole
Metafluid
Transfer matrix method
Metamaterial
Waveguide power-law radius
Reflection coefficient
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Acoustic black hole
Metafluid
Transfer matrix method
Metamaterial
Waveguide power-law radius
Reflection coefficient
Àrees temàtiques de la UPC::Matemàtiques i estadística
description The transfer matrix method has been proposed to analyze the acoustic black hole effect in duct terminations. The latter is achieved by placing a retarding waveguide structure inside the duct, which consists in a set of rings whose inner radii decrease to zero following a power law. The rings are separated by thin air cavities. If the number of ring-cavity ensembles is large enough, wave propagation inside the waveguide can be treated as a continuous problem. A governing differential equation can be derived for the acoustic black hole which intrinsically relies on assumptions from transfer matrix theory. However, no formal demonstration exists showing that the transfer matrix solution is consistent and formally tends to the solution of the continuous problem. Proving such consistency is the main goal of the paper and an original option has been adopted to this purpose. First, we prove the differential equation for the acoustic black hole is identical to the wave equation for a metafluid with a power-law varying density. Transfer matrices are then applied to solve wave propagation in a discretization of the metafluid into layers of constant density. It is shown that when the number of layers tends to infinity and their thicknesses to zero, the transfer matrix solution satisfies the metafluid equation and therefore the acoustic black hole one. The transfer matrices for the metafluid discrete layers take a particularly simple form, which is a great advantage. This work allows one to interpret the retarding waveguide structure as a particular realization of the metafluid.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-01-01
2024
2024-11-28
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/419484
https://dx.doi.org/10.1016/j.apm.2019.09.039
url https://hdl.handle.net/2117/419484
https://dx.doi.org/10.1016/j.apm.2019.09.039
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.81155

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