Multimode Analysis of Geometrically Nonlinear Transverse Free and Forced Vibrations of Tapered Beams
In this study, the geometrically nonlinear free and forced vibrations of tapered beams are investigated on the basis of the Euler-Bernoulli beam theory and the von Karman geometric nonlinearity assumptions. The aim of the analysis is to determine tapered beams nonlinear frequencies and modes, and th...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2022/8464255 |
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| author | Issam El Hantati Ahmed Adri Hatim Fakhreddine Said Rifai Rhali Benamar |
| author_facet | Issam El Hantati Ahmed Adri Hatim Fakhreddine Said Rifai Rhali Benamar |
| author_sort | Issam El Hantati |
| collection | DOAJ |
| description | In this study, the geometrically nonlinear free and forced vibrations of tapered beams are investigated on the basis of the Euler-Bernoulli beam theory and the von Karman geometric nonlinearity assumptions. The aim of the analysis is to determine tapered beams nonlinear frequencies and modes, and the associated stress distributions by means of bending moment diagrams. The linear problem is first solved. Then, to tackle the nonlinear problem, the displacement function is expanded as a series of the linear modes and the discrete expressions for the strain and kinetic energies are derived. Assuming a point excitation of the beam, the algebraic nonlinear system obtained based on Hamilton’s principle is solved by an approximate method. The effect of the geometric nonlinearity in both the free and forced cases was illustrated and discussed and the effect of the variation of various tapered beam geometrical parameters. The effect of varying the excitation level was also examined. |
| format | Article |
| id | doaj-art-243ac41196724bc5bb513ea93a21aba6 |
| institution | OA Journals |
| issn | 1875-9203 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-243ac41196724bc5bb513ea93a21aba62025-08-20T02:04:41ZengWileyShock and Vibration1875-92032022-01-01202210.1155/2022/8464255Multimode Analysis of Geometrically Nonlinear Transverse Free and Forced Vibrations of Tapered BeamsIssam El Hantati0Ahmed Adri1Hatim Fakhreddine2Said Rifai3Rhali Benamar4Laboratory of Mechanics Production and Industrial Engineering (LMPGI)Laboratory of Mechanics Production and Industrial Engineering (LMPGI)Laboratory of Mechanics Production and Industrial Engineering (LMPGI)Laboratory of Mechanics Production and Industrial Engineering (LMPGI)Mohammed V University in RabatIn this study, the geometrically nonlinear free and forced vibrations of tapered beams are investigated on the basis of the Euler-Bernoulli beam theory and the von Karman geometric nonlinearity assumptions. The aim of the analysis is to determine tapered beams nonlinear frequencies and modes, and the associated stress distributions by means of bending moment diagrams. The linear problem is first solved. Then, to tackle the nonlinear problem, the displacement function is expanded as a series of the linear modes and the discrete expressions for the strain and kinetic energies are derived. Assuming a point excitation of the beam, the algebraic nonlinear system obtained based on Hamilton’s principle is solved by an approximate method. The effect of the geometric nonlinearity in both the free and forced cases was illustrated and discussed and the effect of the variation of various tapered beam geometrical parameters. The effect of varying the excitation level was also examined.http://dx.doi.org/10.1155/2022/8464255 |
| spellingShingle | Issam El Hantati Ahmed Adri Hatim Fakhreddine Said Rifai Rhali Benamar Multimode Analysis of Geometrically Nonlinear Transverse Free and Forced Vibrations of Tapered Beams Shock and Vibration |
| title | Multimode Analysis of Geometrically Nonlinear Transverse Free and Forced Vibrations of Tapered Beams |
| title_full | Multimode Analysis of Geometrically Nonlinear Transverse Free and Forced Vibrations of Tapered Beams |
| title_fullStr | Multimode Analysis of Geometrically Nonlinear Transverse Free and Forced Vibrations of Tapered Beams |
| title_full_unstemmed | Multimode Analysis of Geometrically Nonlinear Transverse Free and Forced Vibrations of Tapered Beams |
| title_short | Multimode Analysis of Geometrically Nonlinear Transverse Free and Forced Vibrations of Tapered Beams |
| title_sort | multimode analysis of geometrically nonlinear transverse free and forced vibrations of tapered beams |
| url | http://dx.doi.org/10.1155/2022/8464255 |
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