On the Biharmonic Equation
This article provides a comprehensive introduction to the biharmonic equation, focusing on its origins in elasticity and fluid mechanics. We derive the equation from physical principles of linear deformations and Stokes flow, illustrating its applicability in modeling phenomena such as plate bending...
- Autores:
-
Fierro, A.
Posada, C.
Sanchez, J.J
Martinod T.
- Tipo de recurso:
- Fecha de publicación:
- 2024
- Institución:
- Universidad EAFIT
- Repositorio:
- Repositorio EAFIT
- Idioma:
- eng
- OAI Identifier:
- oai:repository.eafit.edu.co:10784/34774
- Acceso en línea:
- https://hdl.handle.net/10784/34774
- Palabra clave:
- Ecuación Biharmónica
Soluciones Radiales
Separación de Variables
Biharmonic Equation
Radial Solutions
Separation of Variables
- Rights
- License
- Acceso abierto
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Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees2024-11-06T21:43:22Z20242024-11-06T21:43:22Zhttps://hdl.handle.net/10784/34774This article provides a comprehensive introduction to the biharmonic equation, focusing on its origins in elasticity and fluid mechanics. We derive the equation from physical principles of linear deformations and Stokes flow, illustrating its applicability in modeling phenomena such as plate bending and stream functions in viscous media. Solutions are developed in polar and spherical coordinates with radial symmetry, including boundary conditions for spherical domains, as well as in general 2D Cartesian coordinates and the biharmonic wave equation for structural mechanics. Throughout, we highlight practical applications across engineering fields, showcasing the biharmonic equation’s role in predicting stress, displacement, and flow patterns.Este artículo proporciona una introducción completa a la ecuación biharmónica, centrándose en sus orígenes en la elasticidad y la mecánica de fluidos. Derivamos la ecuación a partir de principios físicos de deformaciones lineales y flujo de Stokes, ilustrando su aplicabilidad en el modelado de fenómenos como la flexión de placas y funciones de corriente en medios viscosos. Se desarrollan soluciones en coordenadas polares y esféricas con simetría radial, incluyendo condiciones de contorno para dominios esféricos, así como en coordenadas cartesianas 2D generales y la ecuación de onda biharmónica para la mecánica estructural. A lo largo del texto, destacamos aplicaciones prácticas en diversos campos de la ingeniería, mostrando el papel de la ecuación biharmónica en la predicción de tensiones, desplazamientos y patrones de flujo.application/pdfengOn the Biharmonic EquationSobre la Ecuación BiharmónicaarticleArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501Acceso abiertohttp://purl.org/coar/access_right/c_abf2Ecuación BiharmónicaSoluciones RadialesSeparación de VariablesBiharmonic EquationRadial SolutionsSeparation of VariablesFierro, A.f993250d-5282-44d9-b637-5f087720cfe0-1Posada, C.bc01a6a4-6248-4058-90c0-8701e57f49cb-1Sanchez, J.J43856983-8c01-4b7a-9156-374eb522b5f6-1Martinod T.ae1a3589-6291-4c5e-9b4f-185bcf7fe7b2-1Universidad EAFITCuadernos de Ingeniería Matemática4ORIGINALSobre la Ecuación Biharmónica.pdfArtículo Principalapplication/pdf616391https://repository.eafit.edu.co/bitstreams/b178a4eb-a816-47b2-8bae-699340ebfa7f/downloadb22499c7b65c1971a7b7d103895718ccMD51LICENSELicense.txtLicensetext/plain2584https://repository.eafit.edu.co/bitstreams/afde2dd6-05c8-439d-b2a1-505428953b80/downloaddb71ab3fdf552b62aa0a746cef2840e4MD52THUMBNAILPortada.pngPortadaimage/png1747211https://repository.eafit.edu.co/bitstreams/b8abe796-df1e-4798-ada5-03b78c2b232a/download5bc3017473813e875879dcd10727c474MD5310784/34774oai:repository.eafit.edu.co:10784/347742024-12-04 11:47:37.261open.accesshttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co |
| dc.title.eng.fl_str_mv |
On the Biharmonic Equation |
| dc.title.spa.fl_str_mv |
Sobre la Ecuación Biharmónica |
| title |
On the Biharmonic Equation |
| spellingShingle |
On the Biharmonic Equation Ecuación Biharmónica Soluciones Radiales Separación de Variables Biharmonic Equation Radial Solutions Separation of Variables |
| title_short |
On the Biharmonic Equation |
| title_full |
On the Biharmonic Equation |
| title_fullStr |
On the Biharmonic Equation |
| title_full_unstemmed |
On the Biharmonic Equation |
| title_sort |
On the Biharmonic Equation |
| dc.creator.fl_str_mv |
Fierro, A. Posada, C. Sanchez, J.J Martinod T. |
| dc.contributor.author.none.fl_str_mv |
Fierro, A. Posada, C. Sanchez, J.J Martinod T. |
| dc.contributor.affiliation.spa.fl_str_mv |
Universidad EAFIT |
| dc.subject.keyword.eng.fl_str_mv |
Ecuación Biharmónica Soluciones Radiales Separación de Variables |
| topic |
Ecuación Biharmónica Soluciones Radiales Separación de Variables Biharmonic Equation Radial Solutions Separation of Variables |
| dc.subject.keyword.spa.fl_str_mv |
Biharmonic Equation Radial Solutions Separation of Variables |
| description |
This article provides a comprehensive introduction to the biharmonic equation, focusing on its origins in elasticity and fluid mechanics. We derive the equation from physical principles of linear deformations and Stokes flow, illustrating its applicability in modeling phenomena such as plate bending and stream functions in viscous media. Solutions are developed in polar and spherical coordinates with radial symmetry, including boundary conditions for spherical domains, as well as in general 2D Cartesian coordinates and the biharmonic wave equation for structural mechanics. Throughout, we highlight practical applications across engineering fields, showcasing the biharmonic equation’s role in predicting stress, displacement, and flow patterns. |
| publishDate |
2024 |
| dc.date.available.none.fl_str_mv |
2024-11-06T21:43:22Z |
| dc.date.issued.none.fl_str_mv |
2024 |
| dc.date.accessioned.none.fl_str_mv |
2024-11-06T21:43:22Z |
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article |
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http://purl.org/coar/resource_type/c_6501 |
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Artículo |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/10784/34774 |
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https://hdl.handle.net/10784/34774 |
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eng |
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eng |
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Acceso abierto |
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application/pdf |
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Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees |
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Universidad EAFIT |
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