Periodic solutions of a tapping mode cantilever in an Atomic Force Microscope with harmonic excitation
Resumen:
In this paper, we establish the existence and multiplicity for periodic solutions of the nonlinear system associated with a tapping mode cantilever Atomic Force Microscope (AFM) with Lennard-Jones potential and an external harmonic excitation. The technique used to solve the nonlinear system is based in the classical nonlinear technique of lower and upper solutions in reverse order. Finally, we show some numerical simulations using the Poincaré map to present regions where the existence is guaranteed.
| 2022 | |
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Periodic solution Cantilever vibrations Atomic Force Microscope Lower and upper solutions Singularities Ciencias Naturales y Exactas Matemáticas Matemática Aplicada |
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| Inglés | |
| Universidad Tecnológica | |
| UTEC en REDI | |
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https://hdl.handle.net/20.500.12381/3965
https://doi.org/10.1016/j.cnsns.2022.106396 |
|
| Acceso abierto | |
| Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (CC BY-NC-ND) |
| _version_ | 1879103791915073536 |
|---|---|
| author | Cortés, Daniel |
| author2 | Gutierrez, Alexander Duque, Johan |
| author2_role | author author |
| author_facet | Cortés, Daniel Gutierrez, Alexander Duque, Johan |
| author_role | author |
| bitstream.checksum.fl_str_mv | 8a933bb8545e2fdc33cee758e42ab0be dcd4ae63014857209ccad92a0afa752b |
| bitstream.checksumAlgorithm.fl_str_mv | MD5 MD5 |
| bitstream.url.fl_str_mv | https://redi.anii.org.uy/jspui/bitstream/20.500.12381/3965/2/license.txt https://redi.anii.org.uy/jspui/bitstream/20.500.12381/3965/1/_Periodic%20solutions%20of%20a%20tapping%20mode%20cantilever%20in%20an%20Atomic%20Force%20Microscope%20with%20harmonic%20excitation_%20Duque%2c%20J.pdf |
| collection | UTEC en REDI |
| dc.creator.none.fl_str_mv | Cortés, Daniel Gutierrez, Alexander Duque, Johan |
| dc.date.accessioned.none.fl_str_mv | 2025-05-08T16:03:38Z |
| dc.date.available.none.fl_str_mv | 2025-05-08T16:03:38Z |
| dc.date.issued.none.fl_str_mv | 2022-03 |
| dc.description.abstract.none.fl_txt_mv | In this paper, we establish the existence and multiplicity for periodic solutions of the nonlinear system associated with a tapping mode cantilever Atomic Force Microscope (AFM) with Lennard-Jones potential and an external harmonic excitation. The technique used to solve the nonlinear system is based in the classical nonlinear technique of lower and upper solutions in reverse order. Finally, we show some numerical simulations using the Poincaré map to present regions where the existence is guaranteed. |
| dc.identifier.doi.none.fl_str_mv | https://doi.org/10.1016/j.cnsns.2022.106396 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12381/3965 |
| dc.language.iso.none.fl_str_mv | eng |
| dc.publisher.es.fl_str_mv | Elsevier |
| dc.rights.*.fl_str_mv | Acceso abierto |
| dc.rights.license.none.fl_str_mv | Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (CC BY-NC-ND) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.es.fl_str_mv | Communications in Nonlinear Science and Numerical Simulation, Volume 110 |
| dc.source.none.fl_str_mv | reponame:UTEC en REDI instname:Universidad Tecnológica instacron:Universidad Tecnológica |
| dc.subject.anii.none.fl_str_mv | Ciencias Naturales y Exactas Matemáticas Matemática Aplicada |
| dc.subject.es.fl_str_mv | Periodic solution Cantilever vibrations Atomic Force Microscope Lower and upper solutions Singularities |
| dc.title.none.fl_str_mv | Periodic solutions of a tapping mode cantilever in an Atomic Force Microscope with harmonic excitation |
| dc.type.es.fl_str_mv | Artículo |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/article |
| dc.type.version.es.fl_str_mv | Publicado |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/publishedVersion |
| description | In this paper, we establish the existence and multiplicity for periodic solutions of the nonlinear system associated with a tapping mode cantilever Atomic Force Microscope (AFM) with Lennard-Jones potential and an external harmonic excitation. The technique used to solve the nonlinear system is based in the classical nonlinear technique of lower and upper solutions in reverse order. Finally, we show some numerical simulations using the Poincaré map to present regions where the existence is guaranteed. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | UTEC_1a05bde2950e239d2b08207290c07e7a |
| instacron_str | Universidad Tecnológica |
| institution | Universidad Tecnológica |
| instname_str | Universidad Tecnológica |
| language | eng |
| network_acronym_str | UTEC |
| network_name_str | UTEC en REDI |
| oai_identifier_str | oai:redi.anii.org.uy:20.500.12381/3965 |
| publishDate | 2022 |
| reponame_str | UTEC en REDI |
| repository.mail.fl_str_mv | pablo.montoli@utec.edu.uy |
| repository.name.fl_str_mv | UTEC en REDI - Universidad Tecnológica |
| repository_id_str | 9421_4 |
| rights_invalid_str_mv | Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (CC BY-NC-ND) Acceso abierto |
| spelling | Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional. (CC BY-NC-ND)Acceso abiertoinfo:eu-repo/semantics/openAccess2025-05-08T16:03:38Z2025-05-08T16:03:38Z2022-03https://hdl.handle.net/20.500.12381/3965https://doi.org/10.1016/j.cnsns.2022.106396In this paper, we establish the existence and multiplicity for periodic solutions of the nonlinear system associated with a tapping mode cantilever Atomic Force Microscope (AFM) with Lennard-Jones potential and an external harmonic excitation. The technique used to solve the nonlinear system is based in the classical nonlinear technique of lower and upper solutions in reverse order. Finally, we show some numerical simulations using the Poincaré map to present regions where the existence is guaranteed.engElsevierCommunications in Nonlinear Science and Numerical Simulation, Volume 110reponame:UTEC en REDIinstname:Universidad Tecnológicainstacron:Universidad TecnológicaPeriodic solutionCantilever vibrationsAtomic Force MicroscopeLower and upper solutionsSingularitiesCiencias Naturales y ExactasMatemáticasMatemática AplicadaPeriodic solutions of a tapping mode cantilever in an Atomic Force Microscope with harmonic excitationArtículoPublicadoinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleUniversidad TecnológicaUniversidad Tecnológica de Pereira//Ciencias Naturales y Exactas/Matemáticas/Matemática AplicadaCortés, DanielGutierrez, AlexanderDuque, JohanLICENSElicense.txtlicense.txttext/plain; charset=utf-8814https://redi.anii.org.uy/jspui/bitstream/20.500.12381/3965/2/license.txt8a933bb8545e2fdc33cee758e42ab0beMD52ORIGINAL_Periodic solutions of a tapping mode cantilever in an Atomic Force Microscope with harmonic excitation_ Duque, J.pdf_Periodic solutions of a tapping mode cantilever in an Atomic Force Microscope with harmonic excitation_ Duque, J.pdfapplication/pdf1922365https://redi.anii.org.uy/jspui/bitstream/20.500.12381/3965/1/_Periodic%20solutions%20of%20a%20tapping%20mode%20cantilever%20in%20an%20Atomic%20Force%20Microscope%20with%20harmonic%20excitation_%20Duque%2c%20J.pdfdcd4ae63014857209ccad92a0afa752bMD5120.500.12381/39652025-05-13 14:33:38.2oai:redi.anii.org.uy:20.500.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Institucionalhttps://hdl.handle.net/20.500.12381/3232Universidadhttps://utec.edu.uy/https://redi.anii.org.uy/oai/requestpablo.montoli@utec.edu.uyUruguayopendoar:9421_42025-05-13T17:33:38UTEC en REDI - Universidad Tecnológicafalse |
| spellingShingle | Periodic solutions of a tapping mode cantilever in an Atomic Force Microscope with harmonic excitation Cortés, Daniel Periodic solution Cantilever vibrations Atomic Force Microscope Lower and upper solutions Singularities Ciencias Naturales y Exactas Matemáticas Matemática Aplicada |
| status_str | publishedVersion |
| title | Periodic solutions of a tapping mode cantilever in an Atomic Force Microscope with harmonic excitation |
| title_full | Periodic solutions of a tapping mode cantilever in an Atomic Force Microscope with harmonic excitation |
| title_fullStr | Periodic solutions of a tapping mode cantilever in an Atomic Force Microscope with harmonic excitation |
| title_full_unstemmed | Periodic solutions of a tapping mode cantilever in an Atomic Force Microscope with harmonic excitation |
| title_short | Periodic solutions of a tapping mode cantilever in an Atomic Force Microscope with harmonic excitation |
| title_sort | Periodic solutions of a tapping mode cantilever in an Atomic Force Microscope with harmonic excitation |
| topic | Periodic solution Cantilever vibrations Atomic Force Microscope Lower and upper solutions Singularities Ciencias Naturales y Exactas Matemáticas Matemática Aplicada |
| url | https://hdl.handle.net/20.500.12381/3965 https://doi.org/10.1016/j.cnsns.2022.106396 |
