A generalization of the membrane-plate analogy to non-homogeneous polygonal domains consisting of homogeneous subdomains

Autores
Filipich, Carlos Pedro; Rosales, Marta Beatriz
Año de publicación
2010
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The well-known membrane-plate analogy that relates the natural frequencies when dealing with polygonal homogeneous domains is herein extended to non-homogeneous systems comprised of homogeneous subdomains. The analogy is generalized and demonstrated and it is shown that certain restrictions among the frequency parameters of the membranes and plates arise. Several examples of membranes and plates with interfaces separating areas with different material properties are numerically solved with different approaches. The subdomains are separated by straight, curved, and closed line interfaces. It is shown that the analogy is verified provided that the restrictions are satisfied. The analogy is first demonstrated and presented as a practical methodology to find the natural frequencies of membranes knowing the corresponding ones of the plates or vice versa. Second, the plate and membrane vibration problems, governed by the bi-Laplacian and Laplacian differential operators, respectively, can be solved without distinction, though under certain conditions, i.e., solve one of them and deduce the other using the analogy. Various numerical examples validate the analogy.
Fil: Filipich, Carlos Pedro. Universidad Tecnológica Nacional. Facultad Regional Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina
Fil: Rosales, Marta Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina
Materia
Membranes
Plates
Analogy
Vibration
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/68322
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A generalization of the membrane-plate analogy to non-homogeneous polygonal domains consisting of homogeneous subdomainsFilipich, Carlos PedroRosales, Marta BeatrizMembranesPlatesAnalogyVibrationhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The well-known membrane-plate analogy that relates the natural frequencies when dealing with polygonal homogeneous domains is herein extended to non-homogeneous systems comprised of homogeneous subdomains. The analogy is generalized and demonstrated and it is shown that certain restrictions among the frequency parameters of the membranes and plates arise. Several examples of membranes and plates with interfaces separating areas with different material properties are numerically solved with different approaches. The subdomains are separated by straight, curved, and closed line interfaces. It is shown that the analogy is verified provided that the restrictions are satisfied. The analogy is first demonstrated and presented as a practical methodology to find the natural frequencies of membranes knowing the corresponding ones of the plates or vice versa. Second, the plate and membrane vibration problems, governed by the bi-Laplacian and Laplacian differential operators, respectively, can be solved without distinction, though under certain conditions, i.e., solve one of them and deduce the other using the analogy. Various numerical examples validate the analogy.Fil: Filipich, Carlos Pedro. Universidad Tecnológica Nacional. Facultad Regional Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; ArgentinaFil: Rosales, Marta Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; ArgentinaAcoustical Society of America Institute of Physics2010-04info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/68322Filipich, Carlos Pedro; Rosales, Marta Beatriz; A generalization of the membrane-plate analogy to non-homogeneous polygonal domains consisting of homogeneous subdomains; Acoustical Society of America Institute of Physics; Journal of the Acoustical Society of America; 127; 4; 4-2010; 2295-23000001-4966CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://asa.scitation.org/doi/10.1121/1.3337222info:eu-repo/semantics/altIdentifier/doi/10.1121/1.3337222info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:45:07Zoai:ri.conicet.gov.ar:11336/68322instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-22 11:45:07.774CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A generalization of the membrane-plate analogy to non-homogeneous polygonal domains consisting of homogeneous subdomains
title A generalization of the membrane-plate analogy to non-homogeneous polygonal domains consisting of homogeneous subdomains
spellingShingle A generalization of the membrane-plate analogy to non-homogeneous polygonal domains consisting of homogeneous subdomains
Filipich, Carlos Pedro
Membranes
Plates
Analogy
Vibration
title_short A generalization of the membrane-plate analogy to non-homogeneous polygonal domains consisting of homogeneous subdomains
title_full A generalization of the membrane-plate analogy to non-homogeneous polygonal domains consisting of homogeneous subdomains
title_fullStr A generalization of the membrane-plate analogy to non-homogeneous polygonal domains consisting of homogeneous subdomains
title_full_unstemmed A generalization of the membrane-plate analogy to non-homogeneous polygonal domains consisting of homogeneous subdomains
title_sort A generalization of the membrane-plate analogy to non-homogeneous polygonal domains consisting of homogeneous subdomains
dc.creator.none.fl_str_mv Filipich, Carlos Pedro
Rosales, Marta Beatriz
author Filipich, Carlos Pedro
author_facet Filipich, Carlos Pedro
Rosales, Marta Beatriz
author_role author
author2 Rosales, Marta Beatriz
author2_role author
dc.subject.none.fl_str_mv Membranes
Plates
Analogy
Vibration
topic Membranes
Plates
Analogy
Vibration
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The well-known membrane-plate analogy that relates the natural frequencies when dealing with polygonal homogeneous domains is herein extended to non-homogeneous systems comprised of homogeneous subdomains. The analogy is generalized and demonstrated and it is shown that certain restrictions among the frequency parameters of the membranes and plates arise. Several examples of membranes and plates with interfaces separating areas with different material properties are numerically solved with different approaches. The subdomains are separated by straight, curved, and closed line interfaces. It is shown that the analogy is verified provided that the restrictions are satisfied. The analogy is first demonstrated and presented as a practical methodology to find the natural frequencies of membranes knowing the corresponding ones of the plates or vice versa. Second, the plate and membrane vibration problems, governed by the bi-Laplacian and Laplacian differential operators, respectively, can be solved without distinction, though under certain conditions, i.e., solve one of them and deduce the other using the analogy. Various numerical examples validate the analogy.
Fil: Filipich, Carlos Pedro. Universidad Tecnológica Nacional. Facultad Regional Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina
Fil: Rosales, Marta Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca; Argentina. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina
description The well-known membrane-plate analogy that relates the natural frequencies when dealing with polygonal homogeneous domains is herein extended to non-homogeneous systems comprised of homogeneous subdomains. The analogy is generalized and demonstrated and it is shown that certain restrictions among the frequency parameters of the membranes and plates arise. Several examples of membranes and plates with interfaces separating areas with different material properties are numerically solved with different approaches. The subdomains are separated by straight, curved, and closed line interfaces. It is shown that the analogy is verified provided that the restrictions are satisfied. The analogy is first demonstrated and presented as a practical methodology to find the natural frequencies of membranes knowing the corresponding ones of the plates or vice versa. Second, the plate and membrane vibration problems, governed by the bi-Laplacian and Laplacian differential operators, respectively, can be solved without distinction, though under certain conditions, i.e., solve one of them and deduce the other using the analogy. Various numerical examples validate the analogy.
publishDate 2010
dc.date.none.fl_str_mv 2010-04
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/68322
Filipich, Carlos Pedro; Rosales, Marta Beatriz; A generalization of the membrane-plate analogy to non-homogeneous polygonal domains consisting of homogeneous subdomains; Acoustical Society of America Institute of Physics; Journal of the Acoustical Society of America; 127; 4; 4-2010; 2295-2300
0001-4966
CONICET Digital
CONICET
url http://hdl.handle.net/11336/68322
identifier_str_mv Filipich, Carlos Pedro; Rosales, Marta Beatriz; A generalization of the membrane-plate analogy to non-homogeneous polygonal domains consisting of homogeneous subdomains; Acoustical Society of America Institute of Physics; Journal of the Acoustical Society of America; 127; 4; 4-2010; 2295-2300
0001-4966
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://asa.scitation.org/doi/10.1121/1.3337222
info:eu-repo/semantics/altIdentifier/doi/10.1121/1.3337222
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Acoustical Society of America Institute of Physics
publisher.none.fl_str_mv Acoustical Society of America Institute of Physics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 12.982451

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