A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams

Hantati, Issam El; Adri, Ahmed; Fakhreddine, Hatim; Rifai, Said; Benamar, Rhali

doi:10.1155/2021/6697344

Cited by 3 publications

(3 citation statements)

References 34 publications

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“…The figures below show the effect of the cross-section variations on the frequency ratio. The backbone curves in Figure (3) show that by increasing the maximum non-dimensional amplitude W* max , the frequency ratios also increase. Also, the hardening effect of nonlinearity is more accentuated in beam (b) compared to the other.…”

Section: Present Workmentioning

confidence: 96%

“…A review of the literature goes back to Naguleswaran who presents an overview of the existing studies performed to analyse stepped beams using linear approaches [1]. El Hantati [2], [3] presents a literature review of works related to non-uniform beams in the case of linear and non-linear vibrations. A significant number of studies have been conducted on the dynamic response of single and multi-mass beams, using linear and non-linear analyses for both free and forced vibrations.…”

Section: Introductionmentioning

confidence: 99%

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Geometrically Nonlinear Free Vibrations of Fully Clamped Multi-Stepped Beams Carrying Multiple Masses

Hantati¹,

Adri²,

Fakhreddine³

et al. 2021

Proceedings of the 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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The main objective of this work is to study the geometrically non-linear free vibration of stepped beams carrying multiple masses. These beams are studied on the basis of the Euler-Bernoulli beam theory and the Von Karman geometrical nonlinearity assumptions. The discrete expressions for the beam total strain and kinetic energies are derived. By applying Hamilton's principle, the problem is reduced to a non-linear algebraic system solved by an approximate method (the so-called second formulation). A parametric study is performed to explore the effect of non-linearity on the dynamic behaviour of stepped beams with several added masses. The free vibration case is discussed by considering three types of stepped beams which differ in the cross-section type.

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Section: Present Workmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Geometrically Nonlinear Free Vibrations of Fully Clamped Multi-Stepped Beams Carrying Multiple Masses

Hantati¹,

Adri²,

Fakhreddine³

et al. 2021

Proceedings of the 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…Using the generalized parameterization that corresponds to the transverse displacement of the beam we have [14], [15]:…”

Section: Non-linear Vibration Analysismentioning

confidence: 99%

Analysis of Geometrically Non-Linear Free Vibrations of Functional Graded Beams in a Thermal Environment

Khouddar¹,

Adri²,

Outassafte³

et al. 2021

Proceedings of the 8th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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The thermal non-linear vibrational behavior of functional graded beams is analyzed using Euler-Bernoulli beam theory and Hamilton's theorem, combined with spectral analysis. A set of non-linear equations is derived based on the von Kármán deformation-displacement relationship and the properties of the functional graded material are assumed to be temperature dependent and to follow a simple power distribution in the thickness direction. Numerical solutions of the non-linear dynamic equations of functional graded beams are obtained by an approximate method called the second formulation. In addition, numerical examples were performed to highlight the accuracy of the method used in this study, and the results are very consistent with those found in the literature. In the numerical examples, the influences played by thermal environmental conditions and volume fraction index are discussed in detail.

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Multimode Analysis of Geometrically Nonlinear Transverse Free and Forced Vibrations of Tapered Beams

Hantati

Adri

Fakhreddine

et al. 2022

Shock and Vibration

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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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A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams

Cited by 3 publications

References 34 publications

Geometrically Nonlinear Free Vibrations of Fully Clamped Multi-Stepped Beams Carrying Multiple Masses

Geometrically Nonlinear Free Vibrations of Fully Clamped Multi-Stepped Beams Carrying Multiple Masses

Analysis of Geometrically Non-Linear Free Vibrations of Functional Graded Beams in a Thermal Environment

Multimode Analysis of Geometrically Nonlinear Transverse Free and Forced Vibrations of Tapered Beams

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