FINITE ELEMENT ANALYSIS OF SHEAR-DEFORMATION AND ROTATORY INERTIA FOR BEAM VIBRATION
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Revista Interdisciplinar de Pesquisa em Engenharia |
Texto Completo: | https://periodicos.unb.br/index.php/ripe/article/view/21810 |
Resumo: | Vibration analysis of a beam is an important subject of study in engineering. All real physical structures, when subjected to loads or displacements, behave dynamically. In case of structure with large aspect ratio of height and length the Timoshenko beam theory (TBT) is used, instead of the Euler-Bernoulli theory (EBT), since it takes both shear and rotary inertia into account. Shear effect is extremely large in higher vibration modes due to reduced mode half wave length. In this paper, the full development and analysis of TBT for the transversely vibrating uniform beam are presented for classical boundary condition. Finally, a finite element is developed in terms of dimensionless parameters of rotatory and shear. The stiffness and mass matrices for a two-node beam element with two degree of freedom per node is obtained based upon Hamilton’s principle. Cubic and quadratic Lagrangian polynomials are made interdependent by requiring them to satisfy both of the homogeneous differential equations associated with TBT. Numerical examples are given for some boundary conditions. The results showed that for frequencies above critical frequency, Timoshenko beams presents distinct mode shapes behavior including the presence of double eigenvalues, shear mode or remarkably modes. |
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FINITE ELEMENT ANALYSIS OF SHEAR-DEFORMATION AND ROTATORY INERTIA FOR BEAM VIBRATIONFinite element method. Timoshenko. Critical frequency.Vibration analysis of a beam is an important subject of study in engineering. All real physical structures, when subjected to loads or displacements, behave dynamically. In case of structure with large aspect ratio of height and length the Timoshenko beam theory (TBT) is used, instead of the Euler-Bernoulli theory (EBT), since it takes both shear and rotary inertia into account. Shear effect is extremely large in higher vibration modes due to reduced mode half wave length. In this paper, the full development and analysis of TBT for the transversely vibrating uniform beam are presented for classical boundary condition. Finally, a finite element is developed in terms of dimensionless parameters of rotatory and shear. The stiffness and mass matrices for a two-node beam element with two degree of freedom per node is obtained based upon Hamilton’s principle. Cubic and quadratic Lagrangian polynomials are made interdependent by requiring them to satisfy both of the homogeneous differential equations associated with TBT. Numerical examples are given for some boundary conditions. The results showed that for frequencies above critical frequency, Timoshenko beams presents distinct mode shapes behavior including the presence of double eigenvalues, shear mode or remarkably modes.Programa de Pós-Graduação em Integridade de Materiais da Engenharia2017-08-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.unb.br/index.php/ripe/article/view/2181010.26512/ripe.v2i34.21810Revista Interdisciplinar de Pesquisa em Engenharia; Vol. 2 No. 34 (2016): FINITE ELEMENTS METHODS FORMULATIONS AND NUMERICAL ANALYSIS; 86-103Revista Interdisciplinar de Pesquisa em Engenharia; v. 2 n. 34 (2016): FINITE ELEMENTS METHODS FORMULATIONS AND NUMERICAL ANALYSIS; 86-1032447-6102reponame:Revista Interdisciplinar de Pesquisa em Engenhariainstname:Universidade de Brasília (UnB)instacron:UNBenghttps://periodicos.unb.br/index.php/ripe/article/view/21810/20111Copyright (c) 2019 Revista Interdisciplinar de Pesquisa em Engenharia - RIPEinfo:eu-repo/semantics/openAccessVasconcelos, Ana Carolina AzevedoCosta Azevêdo, Anderson Soares daHoefel, Simone dos Santos2019-06-18T16:11:33Zoai:ojs.pkp.sfu.ca:article/21810Revistahttps://periodicos.unb.br/index.php/ripePUBhttps://periodicos.unb.br/index.php/ripe/oaianflor@unb.br2447-61022447-6102opendoar:2019-06-18T16:11:33Revista Interdisciplinar de Pesquisa em Engenharia - Universidade de Brasília (UnB)false |
dc.title.none.fl_str_mv |
FINITE ELEMENT ANALYSIS OF SHEAR-DEFORMATION AND ROTATORY INERTIA FOR BEAM VIBRATION |
title |
FINITE ELEMENT ANALYSIS OF SHEAR-DEFORMATION AND ROTATORY INERTIA FOR BEAM VIBRATION |
spellingShingle |
FINITE ELEMENT ANALYSIS OF SHEAR-DEFORMATION AND ROTATORY INERTIA FOR BEAM VIBRATION Vasconcelos, Ana Carolina Azevedo Finite element method. Timoshenko. Critical frequency. |
title_short |
FINITE ELEMENT ANALYSIS OF SHEAR-DEFORMATION AND ROTATORY INERTIA FOR BEAM VIBRATION |
title_full |
FINITE ELEMENT ANALYSIS OF SHEAR-DEFORMATION AND ROTATORY INERTIA FOR BEAM VIBRATION |
title_fullStr |
FINITE ELEMENT ANALYSIS OF SHEAR-DEFORMATION AND ROTATORY INERTIA FOR BEAM VIBRATION |
title_full_unstemmed |
FINITE ELEMENT ANALYSIS OF SHEAR-DEFORMATION AND ROTATORY INERTIA FOR BEAM VIBRATION |
title_sort |
FINITE ELEMENT ANALYSIS OF SHEAR-DEFORMATION AND ROTATORY INERTIA FOR BEAM VIBRATION |
author |
Vasconcelos, Ana Carolina Azevedo |
author_facet |
Vasconcelos, Ana Carolina Azevedo Costa Azevêdo, Anderson Soares da Hoefel, Simone dos Santos |
author_role |
author |
author2 |
Costa Azevêdo, Anderson Soares da Hoefel, Simone dos Santos |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Vasconcelos, Ana Carolina Azevedo Costa Azevêdo, Anderson Soares da Hoefel, Simone dos Santos |
dc.subject.por.fl_str_mv |
Finite element method. Timoshenko. Critical frequency. |
topic |
Finite element method. Timoshenko. Critical frequency. |
description |
Vibration analysis of a beam is an important subject of study in engineering. All real physical structures, when subjected to loads or displacements, behave dynamically. In case of structure with large aspect ratio of height and length the Timoshenko beam theory (TBT) is used, instead of the Euler-Bernoulli theory (EBT), since it takes both shear and rotary inertia into account. Shear effect is extremely large in higher vibration modes due to reduced mode half wave length. In this paper, the full development and analysis of TBT for the transversely vibrating uniform beam are presented for classical boundary condition. Finally, a finite element is developed in terms of dimensionless parameters of rotatory and shear. The stiffness and mass matrices for a two-node beam element with two degree of freedom per node is obtained based upon Hamilton’s principle. Cubic and quadratic Lagrangian polynomials are made interdependent by requiring them to satisfy both of the homogeneous differential equations associated with TBT. Numerical examples are given for some boundary conditions. The results showed that for frequencies above critical frequency, Timoshenko beams presents distinct mode shapes behavior including the presence of double eigenvalues, shear mode or remarkably modes. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-08-07 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://periodicos.unb.br/index.php/ripe/article/view/21810 10.26512/ripe.v2i34.21810 |
url |
https://periodicos.unb.br/index.php/ripe/article/view/21810 |
identifier_str_mv |
10.26512/ripe.v2i34.21810 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://periodicos.unb.br/index.php/ripe/article/view/21810/20111 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2019 Revista Interdisciplinar de Pesquisa em Engenharia - RIPE info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2019 Revista Interdisciplinar de Pesquisa em Engenharia - RIPE |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Programa de Pós-Graduação em Integridade de Materiais da Engenharia |
publisher.none.fl_str_mv |
Programa de Pós-Graduação em Integridade de Materiais da Engenharia |
dc.source.none.fl_str_mv |
Revista Interdisciplinar de Pesquisa em Engenharia; Vol. 2 No. 34 (2016): FINITE ELEMENTS METHODS FORMULATIONS AND NUMERICAL ANALYSIS; 86-103 Revista Interdisciplinar de Pesquisa em Engenharia; v. 2 n. 34 (2016): FINITE ELEMENTS METHODS FORMULATIONS AND NUMERICAL ANALYSIS; 86-103 2447-6102 reponame:Revista Interdisciplinar de Pesquisa em Engenharia instname:Universidade de Brasília (UnB) instacron:UNB |
instname_str |
Universidade de Brasília (UnB) |
instacron_str |
UNB |
institution |
UNB |
reponame_str |
Revista Interdisciplinar de Pesquisa em Engenharia |
collection |
Revista Interdisciplinar de Pesquisa em Engenharia |
repository.name.fl_str_mv |
Revista Interdisciplinar de Pesquisa em Engenharia - Universidade de Brasília (UnB) |
repository.mail.fl_str_mv |
anflor@unb.br |
_version_ |
1798315227120402432 |