A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams
The scope of this study is to present a contribution to the geometrically nonlinear free and forced vibration of multiple-stepped beams, based on the theories of Euler–Bernoulli and von Karman, in order to calculate their corresponding amplitude-dependent modes and frequencies. Discrete expressions...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2021/6697344 |
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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 | The scope of this study is to present a contribution to the geometrically nonlinear free and forced vibration of multiple-stepped beams, based on the theories of Euler–Bernoulli and von Karman, in order to calculate their corresponding amplitude-dependent modes and frequencies. Discrete expressions of the strain energy and kinetic energies are derived, and Hamilton’s principle is applied to reduce the problem to a solution of a nonlinear algebraic system and then solved by an approximate method. The forced vibration is then studied based on a multimode approach. The effect of nonlinearity on the dynamic behaviour of multistepped beams in the free and forced vibration is demonstrated and discussed. The effect of varying some geometrical parameters of the stepped beams in the free and forced cases is investigated and illustrated, among which is the variation in the level of excitation. |
| format | Article |
| id | doaj-art-2d7e754ae1144d71bace04a8c8d5c3b1 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-2d7e754ae1144d71bace04a8c8d5c3b12025-02-03T06:05:37ZengWileyShock and Vibration1070-96221875-92032021-01-01202110.1155/2021/66973446697344A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped BeamsIssam El Hantati0Ahmed Adri1Hatim Fakhreddine2Said Rifai3Rhali Benamar4Laboratory of Mechanics Production and Industrial Engineering (LMPGI), High School of Technology (ESTC), Hassan II University of Casablanca, Route d’ElJadida, Km 7, Oasis, Casablanca 8012, MoroccoLaboratory of Mechanics Production and Industrial Engineering (LMPGI), High School of Technology (ESTC), Hassan II University of Casablanca, Route d’ElJadida, Km 7, Oasis, Casablanca 8012, MoroccoLaboratory of Mechanics Production and Industrial Engineering (LMPGI), High School of Technology (ESTC), Hassan II University of Casablanca, Route d’ElJadida, Km 7, Oasis, Casablanca 8012, MoroccoLaboratory of Mechanics Production and Industrial Engineering (LMPGI), High School of Technology (ESTC), Hassan II University of Casablanca, Route d’ElJadida, Km 7, Oasis, Casablanca 8012, MoroccoMohammed V University in Rabat, EMI-Rabat, LERSIM, B.P. 765, Agdal, Rabat, MoroccoThe scope of this study is to present a contribution to the geometrically nonlinear free and forced vibration of multiple-stepped beams, based on the theories of Euler–Bernoulli and von Karman, in order to calculate their corresponding amplitude-dependent modes and frequencies. Discrete expressions of the strain energy and kinetic energies are derived, and Hamilton’s principle is applied to reduce the problem to a solution of a nonlinear algebraic system and then solved by an approximate method. The forced vibration is then studied based on a multimode approach. The effect of nonlinearity on the dynamic behaviour of multistepped beams in the free and forced vibration is demonstrated and discussed. The effect of varying some geometrical parameters of the stepped beams in the free and forced cases is investigated and illustrated, among which is the variation in the level of excitation.http://dx.doi.org/10.1155/2021/6697344 |
| spellingShingle | Issam El Hantati Ahmed Adri Hatim Fakhreddine Said Rifai Rhali Benamar A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams Shock and Vibration |
| title | A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams |
| title_full | A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams |
| title_fullStr | A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams |
| title_full_unstemmed | A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams |
| title_short | A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams |
| title_sort | multimode approach to geometrically nonlinear free and forced vibrations of multistepped beams |
| url | http://dx.doi.org/10.1155/2021/6697344 |
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