Catenary-induced geometric nonlinearity effects on cable linear vibrations

Mansour, Achref; Mekki, Othman Ben; Montassar, Sami; Rega, Giuseppe

doi:10.1016/j.jsv.2017.10.012

Cited by 21 publications

(8 citation statements)

References 15 publications

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“…In fact, few efforts have been devoted to the oscillations of non-shallow cables where the catenary geometry has been adopted to define the static reference configuration [9,10]. Recently, the linear modal properties of arbitrarily sagged and inclined cables have been investigated in the light of a catenary-based model developed analytically by Mansour et al [11]. Taking into account the induced geometric nonlinearity effect, new modal spectrum characterized by higher ratios of internal resonances has been highlighted where non-normal modes are continuously detected.…”

Section: Introductionmentioning

confidence: 99%

Catenary-Based Nonlinear Multimodal Theory of Cable Free Vibrations

Mansour

Rega

Mekki

2020

Nonlinear Dynamics of Structures, Systems and Devices

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Keeping the linear elastic material assumption and accounting for the sole axial extensibility, a new multi-modal theory of cable nonlinear free vibrations is developed analytically, by means of a Galerkin discretization of partial differential equations of motion and the Method of Multiple Scales used to investigate the dynamic behaviour of arbitrarily sagged and inclined cables oscillating around a catenary static profile.

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Section: Introductionmentioning

confidence: 99%

Catenary-Based Nonlinear Multimodal Theory of Cable Free Vibrations

Mansour

Rega

Mekki

2020

Nonlinear Dynamics of Structures, Systems and Devices

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“…Examples of these internal resonances are 1:1 (one-to-one), 2:1 (two-to-one), and 3:1 (three-to-one) resonances. Internal resonances have been studied in different structures, such as beams [2][3][4][5][6], cables [7][8][9][10][11][12], and plates [13].…”

Section: Introductionmentioning

confidence: 99%

Two-to-one internal resonance of an inclined marine riser under harmonic excitations

Alfosail

Younis

2018

Nonlinear Dyn

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In this paper, we study the two-to-one internal resonance of an inclined marine riser under harmonic excitations. The riser is modeled as an Euler-Bernoulli beam accounting for mid-plane stretching, self-weight, and an applied axial top tension. Due to the inclination, the self-weight load causes a static deflection of the riser, which can tune the frequency ratio between the third and first natural frequencies near two. The multiple time scales method is applied to study the nonlinear equation accounting for the system nonlinearity. The solution is then compared to a Galerkin solution showing good agreement. A further investigation is carried out by plotting the frequency response curves, the force response curves, and the steady state response of the multiple scales solution, in addition to the dynamical solution obtained by Galerkin, as they vary with the detuning parameters. The results reveal that the riser vibrations can undergo multiple Hopf bifurcations and experience quasi-periodic motion that can lead to chaotic behavior. These phenomena lead to complex vibrations of the riser, which can accelerate its fatigue failure.

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“…However, through the study on suspended cable, we can find that the symmetric in-plane modes consist of antisymmetric vertical components and symmetric longitudinal components [10,11]. Hence, the phenomenon of frequency crossover occurs, which causes the order exchange of symmetric and antisymmetric modes [12]. Based on this theory, Yu.…”

Section: Introductionmentioning

confidence: 99%

Galloping behavior analysis of transmission line with thin ice accretions

Cui¹,

Liu²,

Zhang³

et al. 2018

Vib. proced.

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A dynamic model of a galloping transmission line able to describe for the coupling of its longitudinal, in-plane, out-of-plane and torsional vibrations is established. It also considers the effects of geometrical nonlinearity and aerodynamic nonlinearity. By the static configuration, the reduced model is obtained. Then, the equations of motion are obtained through the Galerkin method. It contains two in-plane, two out-of-plane and two torsional components. By numerical calculation, the maximum amplitudes at wind speeds are drawn and the galloping behavior of transmission line with thin ice accretions is analyzed. The obtained results show that the second galloping mode is more triggered. The double-mode galloping occurs in all motions, in which the maximum amplitude is bigger than in single-mode galloping. And the double-mode galloping presents the track of inclined '8' in longitudinal direction.

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Catenary-induced geometric nonlinearity effects on cable linear vibrations

Cited by 21 publications

References 15 publications

Catenary-Based Nonlinear Multimodal Theory of Cable Free Vibrations

Catenary-Based Nonlinear Multimodal Theory of Cable Free Vibrations

Two-to-one internal resonance of an inclined marine riser under harmonic excitations

Galloping behavior analysis of transmission line with thin ice accretions

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