A fractional approach to the Fermi-Pasta-Ulam problem

Detalhes bibliográficos
Autor(a) principal: Machado, J. A. Tenreiro
Data de Publicação: 2013
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.22/3762
Resumo: This paper studies the Fermi-Pasta-Ulam problem having in mind the generalization provided by Fractional Calculus (FC). The study starts by addressing the classical formulation, based on the standard integer order differential calculus and evaluates the time and frequency responses. A first generalization to be investigated consists in the direct replacement of the springs by fractional elements of the dissipative type. It is observed that the responses settle rapidly and no relevant phenomena occur. A second approach consists of replacing the springs by a blend of energy extracting and energy inserting elements of symmetrical fractional order with amplitude modulated by quadratic terms. The numerical results reveal a response close to chaotic behaviour.
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spelling A fractional approach to the Fermi-Pasta-Ulam problemThis paper studies the Fermi-Pasta-Ulam problem having in mind the generalization provided by Fractional Calculus (FC). The study starts by addressing the classical formulation, based on the standard integer order differential calculus and evaluates the time and frequency responses. A first generalization to be investigated consists in the direct replacement of the springs by fractional elements of the dissipative type. It is observed that the responses settle rapidly and no relevant phenomena occur. A second approach consists of replacing the springs by a blend of energy extracting and energy inserting elements of symmetrical fractional order with amplitude modulated by quadratic terms. The numerical results reveal a response close to chaotic behaviour.SpringerRepositório Científico do Instituto Politécnico do PortoMachado, J. A. Tenreiro2014-02-06T15:59:02Z20132013-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.22/3762eng1951-635510.1140/epjst/e2013-01964-2metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-03-13T12:43:36Zoai:recipp.ipp.pt:10400.22/3762Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T17:24:45.647977Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv A fractional approach to the Fermi-Pasta-Ulam problem
title A fractional approach to the Fermi-Pasta-Ulam problem
spellingShingle A fractional approach to the Fermi-Pasta-Ulam problem
Machado, J. A. Tenreiro
title_short A fractional approach to the Fermi-Pasta-Ulam problem
title_full A fractional approach to the Fermi-Pasta-Ulam problem
title_fullStr A fractional approach to the Fermi-Pasta-Ulam problem
title_full_unstemmed A fractional approach to the Fermi-Pasta-Ulam problem
title_sort A fractional approach to the Fermi-Pasta-Ulam problem
author Machado, J. A. Tenreiro
author_facet Machado, J. A. Tenreiro
author_role author
dc.contributor.none.fl_str_mv Repositório Científico do Instituto Politécnico do Porto
dc.contributor.author.fl_str_mv Machado, J. A. Tenreiro
description This paper studies the Fermi-Pasta-Ulam problem having in mind the generalization provided by Fractional Calculus (FC). The study starts by addressing the classical formulation, based on the standard integer order differential calculus and evaluates the time and frequency responses. A first generalization to be investigated consists in the direct replacement of the springs by fractional elements of the dissipative type. It is observed that the responses settle rapidly and no relevant phenomena occur. A second approach consists of replacing the springs by a blend of energy extracting and energy inserting elements of symmetrical fractional order with amplitude modulated by quadratic terms. The numerical results reveal a response close to chaotic behaviour.
publishDate 2013
dc.date.none.fl_str_mv 2013
2013-01-01T00:00:00Z
2014-02-06T15:59:02Z
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dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.22/3762
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dc.language.iso.fl_str_mv eng
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10.1140/epjst/e2013-01964-2
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dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
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