Power secant method applied to natural frequency extraction of Timoshenko beam structures
Autor(a) principal: | |
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Data de Publicação: | 2010 |
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=S1679-78252010000300005 |
Resumo: | This work deals with an improved plane frame formulation whose exact dynamic stiffness matrix (DSM) presents, uniquely, null determinant for the natural frequencies. In comparison with the classical DSM, the formulation herein presented has some major advantages: local mode shapes are preserved in the formulation so that, for any positive frequency, the DSM will never be ill-conditioned; in the absence of poles, it is possible to employ the secant method in order to have a more computationally efficient eigenvalue extraction procedure. Applying the procedure to the more general case of Timoshenko beams, we introduce a new technique, named "power deflation", that makes the secant method suitable for the transcendental nonlinear eigenvalue problems based on the improved DSM. In order to avoid overflow occurrences that can hinder the secant method iterations, limiting frequencies are formulated, with scaling also applied to the eigenvalue problem. Comparisons with results available in the literature demonstrate the strength of the proposed method. Computational efficiency is compared with solutions obtained both by FEM and by the Wittrick-Williams algorithm. |
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Latin American journal of solids and structures (Online) |
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Power secant method applied to natural frequency extraction of Timoshenko beam structuresexact modal analysisdynamic stiffness matrixsecant methodpower deflationThis work deals with an improved plane frame formulation whose exact dynamic stiffness matrix (DSM) presents, uniquely, null determinant for the natural frequencies. In comparison with the classical DSM, the formulation herein presented has some major advantages: local mode shapes are preserved in the formulation so that, for any positive frequency, the DSM will never be ill-conditioned; in the absence of poles, it is possible to employ the secant method in order to have a more computationally efficient eigenvalue extraction procedure. Applying the procedure to the more general case of Timoshenko beams, we introduce a new technique, named "power deflation", that makes the secant method suitable for the transcendental nonlinear eigenvalue problems based on the improved DSM. In order to avoid overflow occurrences that can hinder the secant method iterations, limiting frequencies are formulated, with scaling also applied to the eigenvalue problem. Comparisons with results available in the literature demonstrate the strength of the proposed method. Computational efficiency is compared with solutions obtained both by FEM and by the Wittrick-Williams algorithm.Associação Brasileira de Ciências Mecânicas2010-09-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252010000300005Latin American Journal of Solids and Structures v.7 n.3 2010reponame:Latin American journal of solids and structures (Online)instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)instacron:ABCM10.1590/S1679-78252010000300005info:eu-repo/semantics/openAccessDias,C.A.N.eng2012-03-06T00:00:00Zoai:scielo:S1679-78252010000300005Revistahttp://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:2012-03-06T00:00Latin American journal of solids and structures (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)false |
dc.title.none.fl_str_mv |
Power secant method applied to natural frequency extraction of Timoshenko beam structures |
title |
Power secant method applied to natural frequency extraction of Timoshenko beam structures |
spellingShingle |
Power secant method applied to natural frequency extraction of Timoshenko beam structures Dias,C.A.N. exact modal analysis dynamic stiffness matrix secant method power deflation |
title_short |
Power secant method applied to natural frequency extraction of Timoshenko beam structures |
title_full |
Power secant method applied to natural frequency extraction of Timoshenko beam structures |
title_fullStr |
Power secant method applied to natural frequency extraction of Timoshenko beam structures |
title_full_unstemmed |
Power secant method applied to natural frequency extraction of Timoshenko beam structures |
title_sort |
Power secant method applied to natural frequency extraction of Timoshenko beam structures |
author |
Dias,C.A.N. |
author_facet |
Dias,C.A.N. |
author_role |
author |
dc.contributor.author.fl_str_mv |
Dias,C.A.N. |
dc.subject.por.fl_str_mv |
exact modal analysis dynamic stiffness matrix secant method power deflation |
topic |
exact modal analysis dynamic stiffness matrix secant method power deflation |
description |
This work deals with an improved plane frame formulation whose exact dynamic stiffness matrix (DSM) presents, uniquely, null determinant for the natural frequencies. In comparison with the classical DSM, the formulation herein presented has some major advantages: local mode shapes are preserved in the formulation so that, for any positive frequency, the DSM will never be ill-conditioned; in the absence of poles, it is possible to employ the secant method in order to have a more computationally efficient eigenvalue extraction procedure. Applying the procedure to the more general case of Timoshenko beams, we introduce a new technique, named "power deflation", that makes the secant method suitable for the transcendental nonlinear eigenvalue problems based on the improved DSM. In order to avoid overflow occurrences that can hinder the secant method iterations, limiting frequencies are formulated, with scaling also applied to the eigenvalue problem. Comparisons with results available in the literature demonstrate the strength of the proposed method. Computational efficiency is compared with solutions obtained both by FEM and by the Wittrick-Williams algorithm. |
publishDate |
2010 |
dc.date.none.fl_str_mv |
2010-09-01 |
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=S1679-78252010000300005 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252010000300005 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S1679-78252010000300005 |
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.7 n.3 2010 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_ |
1754302886826737664 |