Vibration of non-homogeneous rectangular membranes with arbitrary interfaces

Autores
Filipich, Carlos Pedro; Rosales, Marta Beatriz
Año de publicación
2007
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The study deals with the generalized solution of the title problem. The free vibration problem of a rectangular membrane with partial domains each of uniform density and arbitrary interface is tackled. Previous studies by other researchers include straight parallel to the borders and oblique interfaces, and bent ones. The solution is found by means of a direct variational method with a series composed with a complete set of functions. Two alternative sets are explored: trigonometric and power series. Such series are uniformly convergent to the exact solution. The approach is straightforward and very efficient from the computational viewpoint. A determinant-factorization method is employed to automatically eliminate eventual spurious frequencies. The well-known analogy between plates and membranes does not hold in this problem and a demonstration is included. Diverse illustrations are worked out as the cases of an oblique straight line interface and an open curve line which divides the membrane in two domains each of different density are first presented. Also a rectangular membrane with an interior closed domain is stated and the numerical example of a circular interior zone is included. Comparison between the two alternatives and with other authors' results show excellent agreement. In all cases the computational cost is very low.
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
Vibration
Non-Homogeneous Membrane
Arbitrary Interfaces
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:11336/80067
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Vibration of non-homogeneous rectangular membranes with arbitrary interfacesFilipich, Carlos PedroRosales, Marta BeatrizVibrationNon-Homogeneous MembraneArbitrary InterfacesThe study deals with the generalized solution of the title problem. The free vibration problem of a rectangular membrane with partial domains each of uniform density and arbitrary interface is tackled. Previous studies by other researchers include straight parallel to the borders and oblique interfaces, and bent ones. The solution is found by means of a direct variational method with a series composed with a complete set of functions. Two alternative sets are explored: trigonometric and power series. Such series are uniformly convergent to the exact solution. The approach is straightforward and very efficient from the computational viewpoint. A determinant-factorization method is employed to automatically eliminate eventual spurious frequencies. The well-known analogy between plates and membranes does not hold in this problem and a demonstration is included. Diverse illustrations are worked out as the cases of an oblique straight line interface and an open curve line which divides the membrane in two domains each of different density are first presented. Also a rectangular membrane with an interior closed domain is stated and the numerical example of a circular interior zone is included. Comparison between the two alternatives and with other authors' results show excellent agreement. In all cases the computational cost is very low.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; ArgentinaAcademic Press Ltd - Elsevier Science Ltd2007-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/80067Filipich, Carlos Pedro; Rosales, Marta Beatriz; Vibration of non-homogeneous rectangular membranes with arbitrary interfaces; Academic Press Ltd - Elsevier Science Ltd; Journal of Sound and Vibration; 305; 4-5; 9-2007; 582-5950022-460XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsv.2007.04.021info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022460X07003161info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:27:25Zoai:ri.conicet.gov.ar:11336/80067instacron: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 11:27:25.972CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Vibration of non-homogeneous rectangular membranes with arbitrary interfaces
title Vibration of non-homogeneous rectangular membranes with arbitrary interfaces
spellingShingle Vibration of non-homogeneous rectangular membranes with arbitrary interfaces
Filipich, Carlos Pedro
Vibration
Non-Homogeneous Membrane
Arbitrary Interfaces
title_short Vibration of non-homogeneous rectangular membranes with arbitrary interfaces
title_full Vibration of non-homogeneous rectangular membranes with arbitrary interfaces
title_fullStr Vibration of non-homogeneous rectangular membranes with arbitrary interfaces
title_full_unstemmed Vibration of non-homogeneous rectangular membranes with arbitrary interfaces
title_sort Vibration of non-homogeneous rectangular membranes with arbitrary interfaces
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 Vibration
Non-Homogeneous Membrane
Arbitrary Interfaces
topic Vibration
Non-Homogeneous Membrane
Arbitrary Interfaces
dc.description.none.fl_txt_mv The study deals with the generalized solution of the title problem. The free vibration problem of a rectangular membrane with partial domains each of uniform density and arbitrary interface is tackled. Previous studies by other researchers include straight parallel to the borders and oblique interfaces, and bent ones. The solution is found by means of a direct variational method with a series composed with a complete set of functions. Two alternative sets are explored: trigonometric and power series. Such series are uniformly convergent to the exact solution. The approach is straightforward and very efficient from the computational viewpoint. A determinant-factorization method is employed to automatically eliminate eventual spurious frequencies. The well-known analogy between plates and membranes does not hold in this problem and a demonstration is included. Diverse illustrations are worked out as the cases of an oblique straight line interface and an open curve line which divides the membrane in two domains each of different density are first presented. Also a rectangular membrane with an interior closed domain is stated and the numerical example of a circular interior zone is included. Comparison between the two alternatives and with other authors' results show excellent agreement. In all cases the computational cost is very low.
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 study deals with the generalized solution of the title problem. The free vibration problem of a rectangular membrane with partial domains each of uniform density and arbitrary interface is tackled. Previous studies by other researchers include straight parallel to the borders and oblique interfaces, and bent ones. The solution is found by means of a direct variational method with a series composed with a complete set of functions. Two alternative sets are explored: trigonometric and power series. Such series are uniformly convergent to the exact solution. The approach is straightforward and very efficient from the computational viewpoint. A determinant-factorization method is employed to automatically eliminate eventual spurious frequencies. The well-known analogy between plates and membranes does not hold in this problem and a demonstration is included. Diverse illustrations are worked out as the cases of an oblique straight line interface and an open curve line which divides the membrane in two domains each of different density are first presented. Also a rectangular membrane with an interior closed domain is stated and the numerical example of a circular interior zone is included. Comparison between the two alternatives and with other authors' results show excellent agreement. In all cases the computational cost is very low.
publishDate 2007
dc.date.none.fl_str_mv 2007-09
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/11336/80067
Filipich, Carlos Pedro; Rosales, Marta Beatriz; Vibration of non-homogeneous rectangular membranes with arbitrary interfaces; Academic Press Ltd - Elsevier Science Ltd; Journal of Sound and Vibration; 305; 4-5; 9-2007; 582-595
0022-460X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/80067
identifier_str_mv Filipich, Carlos Pedro; Rosales, Marta Beatriz; Vibration of non-homogeneous rectangular membranes with arbitrary interfaces; Academic Press Ltd - Elsevier Science Ltd; Journal of Sound and Vibration; 305; 4-5; 9-2007; 582-595
0022-460X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsv.2007.04.021
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0022460X07003161
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 Academic Press Ltd - Elsevier Science Ltd
publisher.none.fl_str_mv Academic Press Ltd - Elsevier Science Ltd
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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