Geometrically Non-Linear Free In-Plane Vibration Of Circular Arch Elastically Restrained Against Rotation At The Two Ends

Outassafte, Omar; Adri, Ahmed; Khouddar, Yassine El; Rifai, Said; Benamar, Rhali

doi:10.14445/22315381/ijett-v69i3p215

Cited by 5 publications

(5 citation statements)

References 14 publications

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“…In Figs. 10, the curvature distributions are plotted, associated to the first linear and non-linear deflection, of a C-C shallow arch in free vibration case, for various initial rise (2,4,8) and a maximum non-dimensional amplitudes ( * = 1.5). The corresponding values are summarized in Table 6, in which the percentage correction at the clamps and at the middles are given for various values of initial rise.…”

Section: Resultsmentioning

confidence: 99%

“…Investigating the geometrical non-linearity is one of the major consideration on the design process of the arches. The study of the geometrical non-linearity of a beams, plates ,shells and circular arches were investigated by the authors of [1][2][3][4][5][6][7][8]. The authors classified the arches following their shallowness ratio into two classes; shallow arches and deep or no-shallow arches.…”

Section: Introductionmentioning

confidence: 99%

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Geometrically non-linear free and forced vibration of a shallow arch

Outassafte¹,

Adri²,

Khouddar³

et al. 2021

J. vibroeng.

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The purpose of this present work is to investigate the geometrical non-linearity in free and forced vibration of a shallow arch elastically restrained at the ends. The non-linear governing equilibrium equation of the shallow arch is obtained after the Euler Bernoulli theory and the Von Karman geometrical non-linearity assumptions. After applying the ends conditions, the eigenvalues problem of the generalized trancendant equation have been determined iteratively using the Newton-Raphson algorithm. The kinetic and total strain energy have been discretized into a series of a finite spatial functions which are a combination of linear modes and basic function contribution coefficients. Using Hamilton's principle energy and spectral analysis, the problem is reduced into a set of non-linear algebraic equations that solved numerically using an approximate explicit method developed previously the so-called second formulation. Considering a multimode approach, the effect of initial rise and concentrated force on non-linear behaviour of system has been illustrated in the backbone curves giving the non-linear amplitude-frequency dependence. The corresponding non-linear deflections and curvatures have been plotted for various vibration amplitudes.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Geometrically non-linear free and forced vibration of a shallow arch

Outassafte¹,

Adri²,

Khouddar³

et al. 2021

J. vibroeng.

Self Cite

View full text Add to dashboard Cite

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“…All of the aforementioned studies were carried out assuming linearity and none of them took into account the effect of geometrical non-linearity. This work, which is a continuation of the work previously carried out by Benamar et al [12]- [19], is intended to contribute to a non-linear modal analysis of structural vibration by studying the geometrically non-linear free vibration of stepped beams carrying multiple masses using the Euler-Bernoulli beam theory and the Von Karman geometrical nonlinearity assumptions. The beam total strain and kinetic energies are presented as discrete expressions and then derived.…”

Section: Introductionmentioning

confidence: 95%

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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“…The present work is focused on the study of geometrically non-linear free and forced vibrations of tapered beams and constitutes a continuation of the work previously initiated by Benamar et al [12]- [22] in the perspective of a contribution to a non-linear modal analysis theory of free and forced vibrations of structures. The purpose of this paper is to study the geometrically nonlinear free and forced transverse vibrations of tapered beams with a constant width and a linearly varying depth.…”

Section: Introductionmentioning

confidence: 96%

Geometrically Nonlinear Forced Transver Vibrations Analysis of Tapered Euler-Bernoulli Beams

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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Tapered beams like structures are widely used in many fields including mechanical and civil engineering, such as high-rise buildings, robot arms, etc. The objective of this paper is to study the geometrically nonlinear free and forced transverse vibrations of tapered beams with a constant width and a linearly varying depth. The theoretical model is based on the Euler-Bernoulli beam theory and the Von Kármán assumptions for geometrical nonlinearity. The motion is assumed to be harmonic and the transverse displacement function of the nonlinear beam is expanded as a series of linear modes, determined by solving the linear problem in terms of Bessel functions satisfying the boundary conditions. The discretized expressions for total beam strain and kinetic energies are derived, and by application of Hamilton's principle, the problem is reduced to a non-linear algebraic system solved using a previously developed approximate method (the so-called second formulation). The effect of the linear variation of depth on the non-linear behaviour of the beam is examined and then illustrated. Using the single-mode approach, the non-linear dynamic behaviour of the tapered beam is studied in the forced case. The effects of the excitation level of the applied harmonic force are investigated and illustrated for various scenarios.

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Geometrically Non-Linear Free In-Plane Vibration Of Circular Arch Elastically Restrained Against Rotation At The Two Ends

Cited by 5 publications

References 14 publications

Geometrically non-linear free and forced vibration of a shallow arch

Geometrically non-linear free and forced vibration of a shallow arch

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

Geometrically Nonlinear Forced Transver Vibrations Analysis of Tapered Euler-Bernoulli Beams

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