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Sobre un principio de Ortega y las propiedades de estabilidad lineal de respuestas periódicas con simetrías en osciladores tipo MEMS
dc.rights.license | Atribución-NoComercial-SinDerivadas 4.0 Internacional |
dc.contributor.advisor | Núñez López, Daniel Elias |
dc.contributor.advisor | Casanova Trujillo, Simeón |
dc.contributor.author | Murcia Terranova, Larry |
dc.date.accessioned | 2023-01-18T18:13:11Z |
dc.date.available | 2023-01-18T18:13:11Z |
dc.date.issued | 2022 |
dc.identifier.uri | https://repositorio.unal.edu.co/handle/unal/83013 |
dc.description | graficas, tablas |
dc.description.abstract | En este trabajo se obtiene un novedoso resultado de existencia de respuestas periódicas impares con ciertas propiedades nodales en el contexto de una familia general de osciladores no lineales con simetrías, que en particular tienen aplicaciones en el área de los osciladores tipo MEMS o sistemas micro electromecánicos (Younis, 2011). Más aún, en el contexto de un modelo MEMS electrostático tipo peine con una fuerza restauradora no lineal cúbica, se obtiene un novedoso resultado sobre la existencia de respuestas periódicas impares con ciertas propiedades nodales, y la estabilidad en el sentido lineal de algunas soluciones encontradas cuando la amplitud de la componente AC en el voltaje de entrada es suficientemente pequeña. Algunas simulaciones y resultados de continuación numérica son presentados con el objetivo de validar numéricamente los resultados analíticos para el MEMS tipo peine considerado. Los resultados principales de este trabajo se obtienen mediante la aplicación del principio variacional de R. Ortega (Ortega, 2016), la técnica de truncamiento, cotas a priori de soluciones periódicas para osciladores no lineales y la estrategia perturbativa introducida en (Cen et al., 2020) para la estabilidad en el sentido lineal. (Texto tomado de la fuente) |
dc.description.abstract | In this work a novel result about the existence of odd periodic responses with prescribed nodal properties is introduced for a general family of nonlinear oscillators with symmetries, which have applications in MEMS oscillators or microelectromechanical systems (Younis, 2011). Moreover, in the context of an electrostatic Comb-drive MEMS model with a nonlinear restoring cubic force, a novel result about the existence of odd periodic responses with certain nodal properties, and the stability in the linear sense for some of these solutions is obtained whenever the amplitude of the AC load in the input voltage is small enough. Numerical simulations and numerical continuation results are presented to corroborate the analytical results for this Comb-drive MEMS. The main results of this work are obtained through the application of the variational principle of R. Ortega (Ortega, 2016), the truncation technique, a priori bounds of periodic solutions for nonlinear oscillators and the perturbative approach introduced in (Cen et al.,2020) for the stability in the linear sense. |
dc.format.extent | xi, 123 páginas |
dc.format.mimetype | application/pdf |
dc.language.iso | spa |
dc.publisher | Universidad Nacional de Colombia |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
dc.subject.ddc | 500 - Ciencias naturales y matemáticas::507 - Educación, investigación, temas relacionados |
dc.title | Sobre un principio de Ortega y las propiedades de estabilidad lineal de respuestas periódicas con simetrías en osciladores tipo MEMS |
dc.type | Trabajo de grado - Maestría |
dc.type.driver | info:eu-repo/semantics/masterThesis |
dc.type.version | info:eu-repo/semantics/acceptedVersion |
dc.publisher.program | Manizales - Ciencias Exactas y Naturales - Maestría en Ciencias - Matemática Aplicada |
dc.description.degreelevel | Maestría |
dc.description.degreename | Magíster en Ciencias - Matemática Aplicada |
dc.description.researcharea | Sistemas Dinámicos y Control |
dc.identifier.instname | Universidad Nacional de Colombia |
dc.identifier.reponame | Repositorio Institucional Universidad Nacional de Colombia |
dc.identifier.repourl | https://repositorio.unal.edu.co/ |
dc.publisher.faculty | Facultad de Ciencias Exactas y Naturales |
dc.publisher.place | Manizales, Colombia |
dc.publisher.branch | Universidad Nacional de Colombia - Sede Manizales |
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dc.rights.accessrights | info:eu-repo/semantics/openAccess |
dc.subject.lemb | Sistemas microelectromecánicos -- Costos |
dc.subject.proposal | Soluciones periódicas |
dc.subject.proposal | Osciladores con simetrías |
dc.subject.proposal | Propiedades nodales |
dc.subject.proposal | Estabilidad lineal de soluciones periódicas con simetrías |
dc.subject.proposal | Sistemas micro electromecánicos |
dc.subject.proposal | MEMS |
dc.subject.proposal | Periodic solutions |
dc.subject.proposal | Symmetric oscillators |
dc.subject.proposal | Nodal properties |
dc.subject.proposal | Linear stability of symmetric periodic solutions |
dc.subject.proposal | Microelectromechanical systems |
dc.title.translated | On an Ortega's principle and the linear stability properties of symmetric periodic responses in MEMS oscillators |
dc.type.coar | http://purl.org/coar/resource_type/c_bdcc |
dc.type.coarversion | http://purl.org/coar/version/c_ab4af688f83e57aa |
dc.type.content | Image |
dc.type.content | Text |
oaire.accessrights | http://purl.org/coar/access_right/c_abf2 |
dcterms.audience.professionaldevelopment | Bibliotecarios |
dcterms.audience.professionaldevelopment | Estudiantes |
dcterms.audience.professionaldevelopment | Investigadores |
dcterms.audience.professionaldevelopment | Maestros |
dcterms.audience.professionaldevelopment | Público general |
dc.description.curriculararea | Matemáticas Y Estadística |
dc.contributor.orcid | Murcia Terranova, Larry [0000-0001-9274-0708] |
dc.contributor.scopus | Murcia Terranova, Larry [57223219759] |
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