Nonlinear numerical analysis and averaging method applied atomic force microscopy with viscoelastic term
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/s00419-022-02264-5 http://hdl.handle.net/11449/247664 |
Resumo: | We investigated the nonlinear behavior of an atomic force microscopy system with the contribution of the medium viscoelasticity term. Atomic force microscopy is one of the most used techniques for analyzing the surface topology of samples of interest. We propose a mathematical model for the nonlinear dynamics of the probe and we also assign a term that describes the viscoelasticity of the medium in which the probe is inserted. For our numerical analysis of nonlinear dynamics, we used the Lyapunov Exponent, Bifurcation Diagram, phase maps and Poincaré maps. We also determine a solution for a set of parameters using perturbation theory. In this paper, it is also shown that using higher approximations of averaging method, which allows to solve systems of differential equations with slowly changing variables instead systems with fast change of variables, is very effective to study dynamics of an atomic force microscopy. |
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Nonlinear numerical analysis and averaging method applied atomic force microscopy with viscoelastic termAtomic force microscopyAveraging methodNonlinear dynamicsWe investigated the nonlinear behavior of an atomic force microscopy system with the contribution of the medium viscoelasticity term. Atomic force microscopy is one of the most used techniques for analyzing the surface topology of samples of interest. We propose a mathematical model for the nonlinear dynamics of the probe and we also assign a term that describes the viscoelasticity of the medium in which the probe is inserted. For our numerical analysis of nonlinear dynamics, we used the Lyapunov Exponent, Bifurcation Diagram, phase maps and Poincaré maps. We also determine a solution for a set of parameters using perturbation theory. In this paper, it is also shown that using higher approximations of averaging method, which allows to solve systems of differential equations with slowly changing variables instead systems with fast change of variables, is very effective to study dynamics of an atomic force microscopy.Department of Electrical Universidade Tecnológica Federal do Paraná, PRDepartment of Production Engineering Universidade Tecnológica Federal do Paraná, PRFaculty of Mechanical Engineering of Bauru São Paulo State University, SPVoronezh Federal Research Center Computer Science and Central of Russian Academy of ScienceFaculty of Mechanical Engineering of Bauru São Paulo State University, SPUniversidade Tecnológica Federal do ParanáUniversidade Estadual Paulista (UNESP)Computer Science and Central of Russian Academy of ScienceRibeiro, Mauricio A.Kurina, Galina A.Tusset, Angelo M.Balthazar, Jose M. [UNESP]2023-07-29T13:22:27Z2023-07-29T13:22:27Z2022-12-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article3817-3827http://dx.doi.org/10.1007/s00419-022-02264-5Archive of Applied Mechanics, v. 92, n. 12, p. 3817-3827, 2022.1432-06810939-1533http://hdl.handle.net/11449/24766410.1007/s00419-022-02264-52-s2.0-85138683395Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengArchive of Applied Mechanicsinfo:eu-repo/semantics/openAccess2023-07-29T13:22:28Zoai:repositorio.unesp.br:11449/247664Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462023-07-29T13:22:28Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Nonlinear numerical analysis and averaging method applied atomic force microscopy with viscoelastic term |
title |
Nonlinear numerical analysis and averaging method applied atomic force microscopy with viscoelastic term |
spellingShingle |
Nonlinear numerical analysis and averaging method applied atomic force microscopy with viscoelastic term Ribeiro, Mauricio A. Atomic force microscopy Averaging method Nonlinear dynamics |
title_short |
Nonlinear numerical analysis and averaging method applied atomic force microscopy with viscoelastic term |
title_full |
Nonlinear numerical analysis and averaging method applied atomic force microscopy with viscoelastic term |
title_fullStr |
Nonlinear numerical analysis and averaging method applied atomic force microscopy with viscoelastic term |
title_full_unstemmed |
Nonlinear numerical analysis and averaging method applied atomic force microscopy with viscoelastic term |
title_sort |
Nonlinear numerical analysis and averaging method applied atomic force microscopy with viscoelastic term |
author |
Ribeiro, Mauricio A. |
author_facet |
Ribeiro, Mauricio A. Kurina, Galina A. Tusset, Angelo M. Balthazar, Jose M. [UNESP] |
author_role |
author |
author2 |
Kurina, Galina A. Tusset, Angelo M. Balthazar, Jose M. [UNESP] |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade Tecnológica Federal do Paraná Universidade Estadual Paulista (UNESP) Computer Science and Central of Russian Academy of Science |
dc.contributor.author.fl_str_mv |
Ribeiro, Mauricio A. Kurina, Galina A. Tusset, Angelo M. Balthazar, Jose M. [UNESP] |
dc.subject.por.fl_str_mv |
Atomic force microscopy Averaging method Nonlinear dynamics |
topic |
Atomic force microscopy Averaging method Nonlinear dynamics |
description |
We investigated the nonlinear behavior of an atomic force microscopy system with the contribution of the medium viscoelasticity term. Atomic force microscopy is one of the most used techniques for analyzing the surface topology of samples of interest. We propose a mathematical model for the nonlinear dynamics of the probe and we also assign a term that describes the viscoelasticity of the medium in which the probe is inserted. For our numerical analysis of nonlinear dynamics, we used the Lyapunov Exponent, Bifurcation Diagram, phase maps and Poincaré maps. We also determine a solution for a set of parameters using perturbation theory. In this paper, it is also shown that using higher approximations of averaging method, which allows to solve systems of differential equations with slowly changing variables instead systems with fast change of variables, is very effective to study dynamics of an atomic force microscopy. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-12-01 2023-07-29T13:22:27Z 2023-07-29T13:22:27Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/s00419-022-02264-5 Archive of Applied Mechanics, v. 92, n. 12, p. 3817-3827, 2022. 1432-0681 0939-1533 http://hdl.handle.net/11449/247664 10.1007/s00419-022-02264-5 2-s2.0-85138683395 |
url |
http://dx.doi.org/10.1007/s00419-022-02264-5 http://hdl.handle.net/11449/247664 |
identifier_str_mv |
Archive of Applied Mechanics, v. 92, n. 12, p. 3817-3827, 2022. 1432-0681 0939-1533 10.1007/s00419-022-02264-5 2-s2.0-85138683395 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Archive of Applied Mechanics |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
3817-3827 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1799965433485328384 |