Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity

[EN] In this paper, nonviscous, nonproportional, vibrating structures are considered. Nonviscously damped systems are characterized by dissipative mechanisms which depend on the history of the response velocities via hereditary kernel functions. Solutions of the free motion equation lead to a nonlin...

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Autor: Lázaro, Mario|||0000-0003-4949-8295
Tipo de recurso: artículo
Fecha de publicación:2018
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:10251/124687
Acceso en línea:https://riunet.upv.es/handle/10251/124687
Access Level:acceso abierto
Palabra clave:Nonviscous damping
Nonproportionality
Eigenvalues and eigenvectors
Closed-form expression
Nonclassical damping
Symmetric systems
Viscoelasticity
INGENIERIA AEROESPACIAL
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spelling Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivityLázaro, Mario|||0000-0003-4949-8295Nonviscous dampingNonproportionalityEigenvalues and eigenvectorsClosed-form expressionNonclassical dampingSymmetric systemsViscoelasticityINGENIERIA AEROESPACIAL[EN] In this paper, nonviscous, nonproportional, vibrating structures are considered. Nonviscously damped systems are characterized by dissipative mechanisms which depend on the history of the response velocities via hereditary kernel functions. Solutions of the free motion equation lead to a nonlinear eigenvalue problem involving mass, stiffness and damping matrices. Viscoelasticity leads to a frequency dependence of this latter. In this work, a novel closed-form expression to estimate complex eigenvalues is derived. The key point is to consider the damping model as perturbed by a continuous fictitious parameter. Assuming then the eigensolutions as function of this parameter, the computation of the eigenvalues sensitivity leads to an ordinary differential equation, from whose solution arises the proposed analytical formula. The resulting expression explicitly depends on the viscoelasticity (frequency derivatives of the damping function), the nonproportionality (influence of the modal damping matrix off-diagonal terms). Eigenvectors are obtained using existing methods requiring only the corresponding eigenvalue. The method is validated using a numerical example which compares proposed with exact ones and with those determined from the linear first order approximation in terms of the damping matrix. Frequency response functions are also plotted showing that the proposed approach is valid even for moderately or highly damped systems.ElsevierEscuela Técnica Superior de Ingeniería Aeroespacial y Diseño IndustrialDepartamento de Mecánica de los Medios Continuos y Teoría de EstructurasInstituto Universitario de Matemática Pura y AplicadaRepositorio Institucional de la Universitat Politècnica de València Riunet20182018-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/124687reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1246872026-06-13T07:49:27Z
dc.title.none.fl_str_mv Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity
title Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity
spellingShingle Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity
Lázaro, Mario|||0000-0003-4949-8295
Nonviscous damping
Nonproportionality
Eigenvalues and eigenvectors
Closed-form expression
Nonclassical damping
Symmetric systems
Viscoelasticity
INGENIERIA AEROESPACIAL
title_short Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity
title_full Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity
title_fullStr Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity
title_full_unstemmed Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity
title_sort Closed-form eigensolutions of nonviscously, nonproportionally damped systems based on continuous damping sensitivity
dc.creator.none.fl_str_mv Lázaro, Mario|||0000-0003-4949-8295
author Lázaro, Mario|||0000-0003-4949-8295
author_facet Lázaro, Mario|||0000-0003-4949-8295
author_role author
dc.contributor.none.fl_str_mv 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
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Nonviscous damping
Nonproportionality
Eigenvalues and eigenvectors
Closed-form expression
Nonclassical damping
Symmetric systems
Viscoelasticity
INGENIERIA AEROESPACIAL
topic Nonviscous damping
Nonproportionality
Eigenvalues and eigenvectors
Closed-form expression
Nonclassical damping
Symmetric systems
Viscoelasticity
INGENIERIA AEROESPACIAL
description [EN] In this paper, nonviscous, nonproportional, vibrating structures are considered. Nonviscously damped systems are characterized by dissipative mechanisms which depend on the history of the response velocities via hereditary kernel functions. Solutions of the free motion equation lead to a nonlinear eigenvalue problem involving mass, stiffness and damping matrices. Viscoelasticity leads to a frequency dependence of this latter. In this work, a novel closed-form expression to estimate complex eigenvalues is derived. The key point is to consider the damping model as perturbed by a continuous fictitious parameter. Assuming then the eigensolutions as function of this parameter, the computation of the eigenvalues sensitivity leads to an ordinary differential equation, from whose solution arises the proposed analytical formula. The resulting expression explicitly depends on the viscoelasticity (frequency derivatives of the damping function), the nonproportionality (influence of the modal damping matrix off-diagonal terms). Eigenvectors are obtained using existing methods requiring only the corresponding eigenvalue. The method is validated using a numerical example which compares proposed with exact ones and with those determined from the linear first order approximation in terms of the damping matrix. Frequency response functions are also plotted showing that the proposed approach is valid even for moderately or highly damped systems.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-01-01
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/10251/124687
url https://riunet.upv.es/handle/10251/124687
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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
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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score 15,300724

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