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: Issam El Hantati, Ahmed Adri, Hatim Fakhreddine, Said Rifai, Rhali Benamar
Format: Article
Language:English
Published: Wiley 2022-01-01
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.
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issn 1875-9203
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publishDate 2022-01-01
publisher Wiley
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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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