Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams

Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams

Abstract In this paper, the Homotopy Analysis Method (HAM) with two auxiliary parameters and Differential Transform Method (DTM) are employed to solve the geometric nonlinear vibration of Euler-Bernoulli beams subjected to axial loads. A second auxiliary parameter is applied to the HAM to improve convergence in nonlinear systems with large deformations. The results from HAM and DTM are compared with another popular numerical method, the shooting method, to validate these two analytical methods. HAM and DTM show excellent agreement with numerical results (the maximum errors in our calculations are about 0.002%), and they additionally provide a simple way to conduct a parametric analysis with different physical parameters in Euler-Bernoulli beams. To show the benefits of this method, the effect of different physical parameters on the amplitude is discussed for a cantilever beam with a cyclically varying axial load.

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Main Authors: Jafari,S.S., Rashidi,M.M., Johnson,S.
Format: Digital revista
Language:English
Published: Associação Brasileira de Ciências Mecânicas 2016
Online Access:http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016000701250
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spelling oai:scielo:S1679-782520160007012502016-07-25Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli BeamsJafari,S.S.Rashidi,M.M.Johnson,S. Nonlinear vibration Euler-Bernoulli beam Homotopy Analysis Method (HAM) Two auxiliary parameters Differential Transform Method (DTM) Abstract In this paper, the Homotopy Analysis Method (HAM) with two auxiliary parameters and Differential Transform Method (DTM) are employed to solve the geometric nonlinear vibration of Euler-Bernoulli beams subjected to axial loads. A second auxiliary parameter is applied to the HAM to improve convergence in nonlinear systems with large deformations. The results from HAM and DTM are compared with another popular numerical method, the shooting method, to validate these two analytical methods. HAM and DTM show excellent agreement with numerical results (the maximum errors in our calculations are about 0.002%), and they additionally provide a simple way to conduct a parametric analysis with different physical parameters in Euler-Bernoulli beams. To show the benefits of this method, the effect of different physical parameters on the amplitude is discussed for a cantilever beam with a cyclically varying axial load.info:eu-repo/semantics/openAccessAssociação Brasileira de Ciências MecânicasLatin American Journal of Solids and Structures v.13 n.7 20162016-07-01info:eu-repo/semantics/articletext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016000701250en10.1590/1679-78252437
institution SCIELO
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country Brasil
countrycode BR
component Revista
access En linea
databasecode rev-scielo-br
tag revista
region America del Sur
libraryname SciELO
language English
format Digital
author Jafari,S.S.
Rashidi,M.M.
Johnson,S.
spellingShingle Jafari,S.S.
Rashidi,M.M.
Johnson,S.
Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams
author_facet Jafari,S.S.
Rashidi,M.M.
Johnson,S.
author_sort Jafari,S.S.
title Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams
title_short Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams
title_full Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams
title_fullStr Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams
title_full_unstemmed Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams
title_sort analytical approximation of nonlinear vibration of euler-bernoulli beams
description Abstract In this paper, the Homotopy Analysis Method (HAM) with two auxiliary parameters and Differential Transform Method (DTM) are employed to solve the geometric nonlinear vibration of Euler-Bernoulli beams subjected to axial loads. A second auxiliary parameter is applied to the HAM to improve convergence in nonlinear systems with large deformations. The results from HAM and DTM are compared with another popular numerical method, the shooting method, to validate these two analytical methods. HAM and DTM show excellent agreement with numerical results (the maximum errors in our calculations are about 0.002%), and they additionally provide a simple way to conduct a parametric analysis with different physical parameters in Euler-Bernoulli beams. To show the benefits of this method, the effect of different physical parameters on the amplitude is discussed for a cantilever beam with a cyclically varying axial load.
publisher Associação Brasileira de Ciências Mecânicas
publishDate 2016
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016000701250
work_keys_str_mv AT jafariss analyticalapproximationofnonlinearvibrationofeulerbernoullibeams
AT rashidimm analyticalapproximationofnonlinearvibrationofeulerbernoullibeams
AT johnsons analyticalapproximationofnonlinearvibrationofeulerbernoullibeams
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