Analytical solution for nonlinear dynamic behavior of viscoelastic nano-plates modeled by consistent couple stress theory
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Latin American journal of solids and structures (Online) |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252018000900508 |
Resumo: | Abstract This paper analyses the non-stationary free vibration and nonlinear dynamic behavior of the viscoelastic nano-plates. For this purpose, a size-dependent theory is developed in the framework of the consistent couple stress theory for viscoelastic materials. The previously presented modified couple stress theory was based on some consideration making it partially doubtful to apply. This paper uses the recent findings for the mentioned problem and develops it to analyze the nonlinear dynamic behavior of nano-plates with nonlinear viscoelasticity. The material is supposed to follow the Leaderman integral nonlinear constitutive relation. In order to capture the geometrical nonlinearity, the von-Karman strain displacement relation is used. The viscous parts of the size-independent and size-dependent stress tensors are calculated in the framework of the Leaderman integral and the resultant virtual work terms are obtained. The governing equations of motion are derived using the Hamilton principle in the form of the nonlinear second order integro-partial differential equation with coupled terms. These coupled size-dependent viscoelastic equations are solved using the forth-order Runge-kutta and Harmonic balance method after simplifying by the expansion theory. The short-time Fourier transform is performed to examine the system free vibration. In addition, frequency- and force-responses of the nanosystem subjected to distribute harmonic load are presented. The obtained results show that the viscoelastic model-based vibration is non-stationary unlike the elastic model. Moreover, the damping mechanism of the viscoelasticity is amplitude dependent and the contribution of the viscoelastic damping terms at higher forcing conditions becomes noticeable. |
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Latin American journal of solids and structures (Online) |
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Analytical solution for nonlinear dynamic behavior of viscoelastic nano-plates modeled by consistent couple stress theorynonlinear viscoelasticconsistent couple stressHarmonic balance methodnonlinear dynamicnano-plateAbstract This paper analyses the non-stationary free vibration and nonlinear dynamic behavior of the viscoelastic nano-plates. For this purpose, a size-dependent theory is developed in the framework of the consistent couple stress theory for viscoelastic materials. The previously presented modified couple stress theory was based on some consideration making it partially doubtful to apply. This paper uses the recent findings for the mentioned problem and develops it to analyze the nonlinear dynamic behavior of nano-plates with nonlinear viscoelasticity. The material is supposed to follow the Leaderman integral nonlinear constitutive relation. In order to capture the geometrical nonlinearity, the von-Karman strain displacement relation is used. The viscous parts of the size-independent and size-dependent stress tensors are calculated in the framework of the Leaderman integral and the resultant virtual work terms are obtained. The governing equations of motion are derived using the Hamilton principle in the form of the nonlinear second order integro-partial differential equation with coupled terms. These coupled size-dependent viscoelastic equations are solved using the forth-order Runge-kutta and Harmonic balance method after simplifying by the expansion theory. The short-time Fourier transform is performed to examine the system free vibration. In addition, frequency- and force-responses of the nanosystem subjected to distribute harmonic load are presented. The obtained results show that the viscoelastic model-based vibration is non-stationary unlike the elastic model. Moreover, the damping mechanism of the viscoelasticity is amplitude dependent and the contribution of the viscoelastic damping terms at higher forcing conditions becomes noticeable.Associação Brasileira de Ciências Mecânicas2018-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252018000900508Latin American Journal of Solids and Structures v.15 n.9 2018reponame:Latin American journal of solids and structures (Online)instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)instacron:ABCM10.1590/1679-78254918info:eu-repo/semantics/openAccessAjri,MasoudFakhrabadi,Mir Masoud SeyyedRastgoo,Abbaseng2018-09-13T00:00:00Zoai:scielo:S1679-78252018000900508Revistahttp://www.scielo.br/scielo.php?script=sci_serial&pid=1679-7825&lng=pt&nrm=isohttps://old.scielo.br/oai/scielo-oai.phpabcm@abcm.org.br||maralves@usp.br1679-78251679-7817opendoar:2018-09-13T00:00Latin American journal of solids and structures (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)false |
dc.title.none.fl_str_mv |
Analytical solution for nonlinear dynamic behavior of viscoelastic nano-plates modeled by consistent couple stress theory |
title |
Analytical solution for nonlinear dynamic behavior of viscoelastic nano-plates modeled by consistent couple stress theory |
spellingShingle |
Analytical solution for nonlinear dynamic behavior of viscoelastic nano-plates modeled by consistent couple stress theory Ajri,Masoud nonlinear viscoelastic consistent couple stress Harmonic balance method nonlinear dynamic nano-plate |
title_short |
Analytical solution for nonlinear dynamic behavior of viscoelastic nano-plates modeled by consistent couple stress theory |
title_full |
Analytical solution for nonlinear dynamic behavior of viscoelastic nano-plates modeled by consistent couple stress theory |
title_fullStr |
Analytical solution for nonlinear dynamic behavior of viscoelastic nano-plates modeled by consistent couple stress theory |
title_full_unstemmed |
Analytical solution for nonlinear dynamic behavior of viscoelastic nano-plates modeled by consistent couple stress theory |
title_sort |
Analytical solution for nonlinear dynamic behavior of viscoelastic nano-plates modeled by consistent couple stress theory |
author |
Ajri,Masoud |
author_facet |
Ajri,Masoud Fakhrabadi,Mir Masoud Seyyed Rastgoo,Abbas |
author_role |
author |
author2 |
Fakhrabadi,Mir Masoud Seyyed Rastgoo,Abbas |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Ajri,Masoud Fakhrabadi,Mir Masoud Seyyed Rastgoo,Abbas |
dc.subject.por.fl_str_mv |
nonlinear viscoelastic consistent couple stress Harmonic balance method nonlinear dynamic nano-plate |
topic |
nonlinear viscoelastic consistent couple stress Harmonic balance method nonlinear dynamic nano-plate |
description |
Abstract This paper analyses the non-stationary free vibration and nonlinear dynamic behavior of the viscoelastic nano-plates. For this purpose, a size-dependent theory is developed in the framework of the consistent couple stress theory for viscoelastic materials. The previously presented modified couple stress theory was based on some consideration making it partially doubtful to apply. This paper uses the recent findings for the mentioned problem and develops it to analyze the nonlinear dynamic behavior of nano-plates with nonlinear viscoelasticity. The material is supposed to follow the Leaderman integral nonlinear constitutive relation. In order to capture the geometrical nonlinearity, the von-Karman strain displacement relation is used. The viscous parts of the size-independent and size-dependent stress tensors are calculated in the framework of the Leaderman integral and the resultant virtual work terms are obtained. The governing equations of motion are derived using the Hamilton principle in the form of the nonlinear second order integro-partial differential equation with coupled terms. These coupled size-dependent viscoelastic equations are solved using the forth-order Runge-kutta and Harmonic balance method after simplifying by the expansion theory. The short-time Fourier transform is performed to examine the system free vibration. In addition, frequency- and force-responses of the nanosystem subjected to distribute harmonic load are presented. The obtained results show that the viscoelastic model-based vibration is non-stationary unlike the elastic model. Moreover, the damping mechanism of the viscoelasticity is amplitude dependent and the contribution of the viscoelastic damping terms at higher forcing conditions becomes noticeable. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-01-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252018000900508 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252018000900508 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/1679-78254918 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Associação Brasileira de Ciências Mecânicas |
publisher.none.fl_str_mv |
Associação Brasileira de Ciências Mecânicas |
dc.source.none.fl_str_mv |
Latin American Journal of Solids and Structures v.15 n.9 2018 reponame:Latin American journal of solids and structures (Online) instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM) instacron:ABCM |
instname_str |
Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM) |
instacron_str |
ABCM |
institution |
ABCM |
reponame_str |
Latin American journal of solids and structures (Online) |
collection |
Latin American journal of solids and structures (Online) |
repository.name.fl_str_mv |
Latin American journal of solids and structures (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM) |
repository.mail.fl_str_mv |
abcm@abcm.org.br||maralves@usp.br |
_version_ |
1754302889663135744 |