Critical relationships in nonviscous systems with proportional damping

[EN] Materials with time-dependent dissipative behavior currently play an important role in the design of new mechanisms for vibration control in civil, automotive, aeronautical and mechanical engineering. Damping forces are assumed to depend on the past history of the velocity response via convolut...

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Autores: Lázaro, Mario|||0000-0003-4949-8295, García-Raffi, L. M.|||0000-0003-3985-8453
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/166847
Acceso en línea:https://riunet.upv.es/handle/10251/166847
Access Level:acceso abierto
Palabra clave:Viscoelastic systems
Nonviscous systems
Critical damping
Eigenvalues
Proportional damping
MATEMATICA APLICADA
INGENIERIA AEROESPACIAL
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spelling Critical relationships in nonviscous systems with proportional dampingLázaro, Mario|||0000-0003-4949-8295García-Raffi, L. M.|||0000-0003-3985-8453Viscoelastic systemsNonviscous systemsCritical dampingEigenvaluesProportional dampingMATEMATICA APLICADAINGENIERIA AEROESPACIAL[EN] Materials with time-dependent dissipative behavior currently play an important role in the design of new mechanisms for vibration control in civil, automotive, aeronautical and mechanical engineering. Damping forces are assumed to depend on the past history of the velocity response via convolution integrals over multiple exponential hereditary kernels. Hence, the computational complexity increases both in time and frequency domain with respect to the widely used viscous models. The derivations of this article are carried out under the hypothesis of nonviscous proportional damping, that is, the time-dependent damping matrix becomes diagonal in the modal space of the undamped system. In this context, the damping parameters, which control the behavior of dissipative forces, will be considered as variable. Critical manifolds can be defined as hypersurfaces in the domain of the damping parameters, which represent boundaries between oscillatory and non-oscillatory motion. In particular, critical manifolds of two parameters are the so-called critical curves. In this paper a new method to obtain critical curves in proportionally damped nonviscous multiple degree-of-freedom systems is presented. It is proved that the conditions of critical damping lead to relationships that enables an analytical determination of such critical curves, in parametric form. In addtion, it is demonstrated that modal critical regions arise as the intersection of the critical curves. The proposed method is validated through two numerical examples involving discrete and continuous system with generalized proportional damping. (C) 2020 Elsevier Ltd. All rights reserved.This research was partially supported by the project HYPERMETA funded under the program Etoiles Montantes of the Region Pays de la Loire (France).ElsevierDepartamento de Matemática AplicadaEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialDepartamento de Mecánica de los Medios Continuos y Teoría de EstructurasInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería de Caminos, Canales y PuertosRegion Pays de la LoireRepositorio Institucional de la Universitat Politècnica de València Riunet20202020-10-27journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/166847reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1668472026-06-13T07:49:27Z
dc.title.none.fl_str_mv Critical relationships in nonviscous systems with proportional damping
title Critical relationships in nonviscous systems with proportional damping
spellingShingle Critical relationships in nonviscous systems with proportional damping
Lázaro, Mario|||0000-0003-4949-8295
Viscoelastic systems
Nonviscous systems
Critical damping
Eigenvalues
Proportional damping
MATEMATICA APLICADA
INGENIERIA AEROESPACIAL
title_short Critical relationships in nonviscous systems with proportional damping
title_full Critical relationships in nonviscous systems with proportional damping
title_fullStr Critical relationships in nonviscous systems with proportional damping
title_full_unstemmed Critical relationships in nonviscous systems with proportional damping
title_sort Critical relationships in nonviscous systems with proportional damping
dc.creator.none.fl_str_mv Lázaro, Mario|||0000-0003-4949-8295
García-Raffi, L. M.|||0000-0003-3985-8453
author Lázaro, Mario|||0000-0003-4949-8295
author_facet Lázaro, Mario|||0000-0003-4949-8295
García-Raffi, L. M.|||0000-0003-3985-8453
author_role author
author2 García-Raffi, L. M.|||0000-0003-3985-8453
author2_role author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Escuela Técnica Superior de Ingeniería Aeroespacial y Diseño Industrial
Departamento de Mecánica de los Medios Continuos y Teoría de Estructuras
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería de Caminos, Canales y Puertos
Region Pays de la Loire
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Viscoelastic systems
Nonviscous systems
Critical damping
Eigenvalues
Proportional damping
MATEMATICA APLICADA
INGENIERIA AEROESPACIAL
topic Viscoelastic systems
Nonviscous systems
Critical damping
Eigenvalues
Proportional damping
MATEMATICA APLICADA
INGENIERIA AEROESPACIAL
description [EN] Materials with time-dependent dissipative behavior currently play an important role in the design of new mechanisms for vibration control in civil, automotive, aeronautical and mechanical engineering. Damping forces are assumed to depend on the past history of the velocity response via convolution integrals over multiple exponential hereditary kernels. Hence, the computational complexity increases both in time and frequency domain with respect to the widely used viscous models. The derivations of this article are carried out under the hypothesis of nonviscous proportional damping, that is, the time-dependent damping matrix becomes diagonal in the modal space of the undamped system. In this context, the damping parameters, which control the behavior of dissipative forces, will be considered as variable. Critical manifolds can be defined as hypersurfaces in the domain of the damping parameters, which represent boundaries between oscillatory and non-oscillatory motion. In particular, critical manifolds of two parameters are the so-called critical curves. In this paper a new method to obtain critical curves in proportionally damped nonviscous multiple degree-of-freedom systems is presented. It is proved that the conditions of critical damping lead to relationships that enables an analytical determination of such critical curves, in parametric form. In addtion, it is demonstrated that modal critical regions arise as the intersection of the critical curves. The proposed method is validated through two numerical examples involving discrete and continuous system with generalized proportional damping. (C) 2020 Elsevier Ltd. All rights reserved.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-10-27
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/166847
url https://riunet.upv.es/handle/10251/166847
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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