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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/68322
Ver los metadatos del registro completo
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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 Técnicas2025-09-29T10:14:52Zoai: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:34982025-09-29 10:14:52.478CONICET 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 |
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CONICET Digital (CONICET) |
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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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1844614080529170432 |
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13.070432 |