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 co...
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| Format: | Article |
| Language: | English |
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Marcílio Alves
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| Series: | Latin American Journal of Solids and Structures |
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| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016000701250&lng=en&tlng=en |
| _version_ | 1819042248703082496 |
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| author | S.S. Jafari M.M. Rashidi S. Johnson |
| author_facet | S.S. Jafari M.M. Rashidi S. Johnson |
| author_sort | S.S. Jafari |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-21T09:37:53Z |
| format | Article |
| id | doaj.art-83162a9efa7c473a97a9a263fd8133e5 |
| institution | Directory Open Access Journal |
| issn | 1679-7825 |
| language | English |
| last_indexed | 2024-12-21T09:37:53Z |
| publisher | Marcílio Alves |
| record_format | Article |
| series | Latin American Journal of Solids and Structures |
| spelling | doaj.art-83162a9efa7c473a97a9a263fd8133e52022-12-21T19:08:34ZengMarcílio AlvesLatin American Journal of Solids and Structures1679-78251371250126410.1590/1679-78252437S1679-78252016000701250Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli BeamsS.S. JafariM.M. RashidiS. JohnsonAbstract 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.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016000701250&lng=en&tlng=enNonlinear vibrationEuler-Bernoulli beamHomotopy Analysis Method (HAM)Two auxiliary parametersDifferential Transform Method (DTM) |
| spellingShingle | S.S. Jafari M.M. Rashidi S. Johnson Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams Latin American Journal of Solids and Structures Nonlinear vibration Euler-Bernoulli beam Homotopy Analysis Method (HAM) Two auxiliary parameters Differential Transform Method (DTM) |
| title | 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_short | Analytical Approximation of Nonlinear Vibration of Euler-Bernoulli Beams |
| title_sort | analytical approximation of nonlinear vibration of euler bernoulli beams |
| topic | Nonlinear vibration Euler-Bernoulli beam Homotopy Analysis Method (HAM) Two auxiliary parameters Differential Transform Method (DTM) |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1679-78252016000701250&lng=en&tlng=en |
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