Three-dimensional non-linear coupling and dynamic tension in the large-amplitude free vibrations of arbitrarily sagged cables

Srinil, Narakorn; Rega, Giuseppe; Chucheepsakul, Somchai

doi:10.1016/s0022-460x(03)00137-8

Cited by 74 publications

(78 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By means of the variational formulation, the governing exact PDEs of 3-D coupled undamped unforced motion of the cable about its static equilibrium read [20,21,31]:…”

Section: Exact Equations Of Motionmentioning

confidence: 99%

“…This system is highly nonlinear and its closedform analytical solution cannot be sought. Hence, either a direct numerical [14,21] or an approximate analytical solution based on some assumptions has to be pursued.…”

Section: Exact Equations Of Motionmentioning

confidence: 99%

“…Subsequently, based on Equations (15), (21) with k = 2, (25a) and (29), the polar form for A m , the relationship ω s = 2ω r + εσ and the solutions of β r and β s from Equations (37) and (39), the second-order coupled longitudinal and vertical (J = 1 and 2) dynamic displacements of an internally resonant horizontal/inclined cable are expressed as…”

Section: Steady-state Resonantly Coupled Motionsmentioning

confidence: 99%

“…To overcome some of the aforementioned issues, either analytical/numerical [19] or purely numerical [20,21] approaches have been used for investigating some important aspects of the response of noncondensed, multi-dimensional, arbitrarily sagged, or inclined cables whose theoretical formulation relies on exact kinematic modeling. Alternatively, refined analytical techniques -still applied to the parabolic condensed horizontal cable -have been proposed to improve the (iii) issue.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part I: Theoretical formulation and model validation

2006

Self Cite

View full text Add to dashboard Cite

Αβστραχτ. Τηισ παπερ ισ τηε φιρστ οφ τωο παπερσ δεαλινγ ωιτη αναλψτιχαλ ινϖεστιγατιον οφ ρεσοναντ mυλτι−mοδαλ δψναmιχσ δυε το 2:1 ιντερναλ ρεσονανχεσ ιν τηε φινιτε−αmπλιτυδε φρεε ϖιβρατιονσ οφ ηοριζονταλ/ινχλινεδ χαβλεσ. Παρτ Ι ισ χονχερνεδ ωιτη τηεορετιχαλ φορmυλατιον ανδ ϖαλιδατιον οφ τηε γενεραλ χαβλε mοδελ. Αππροξιmατε νον−λινεαρ παρτιαλ διφφερεντιαλ εθυατιονσ οφ 3−D χουπλεδ mοτιον οφ σmαλλ σαγγεδ χαβλεσ -ωηιχη αχχουντ φορ βοτη σπατιο−τεmποραλ ϖαριατιον οφ νον−λινεαρ δψναmιχ τενσιον ανδ σψστεm ασψmmετρψ δυε το ινχλινεδ σαγγεδ χονφιγυρατιονσ -αρε πρεσεντεδ. Α mυλτι−διmενσιοναλ Γαλερκιν εξπανσιον οφ τηε σολυτιον οφ νον−πλαναρ/πλαναρ mοτιον ισ περφορmεδ, ψιελδινγ α χοmπλετε σετ οφ σψστεm θυαδρατιχ/χυβιχ χοεφφιχιεντσ. Wιτη τηε αιm οφ παραmετριχαλλψ στυδψινγ τηε βεηαϖιορ οφ ηοριζονταλ/ινχλινεδ χαβλεσ ιν Παρτ ΙΙ [1], α σεχονδ−ορδερ ασψmπτοτιχ αναλψσισ υνδερ πλαναρ 2:1 ρεσονανχε ισ αχχοmπλισηεδ βψ τηε mετηοδ οφ mυλτιπλε σχαλεσ. Ον αχχουντινγ φορ ηιγηερ−ορδερ εφφεχτσ οφ θυαδρατιχ/χυβιχ νονλινεαριτιεσ, αππροξιmατε χλοσεδ−φορm σολυτιονσ οφ νον−λινεαρ αmπλιτυδεσ, φρεθυενχιεσ ανδ δψναmιχ χονφιγυρατιονσ οφ ρεσοναντ νον− λινεαρ νορmαλ mοδεσ ρεϖεαλ τηε δεπενδενχε οφ χαβλε ρεσπονσε ον ρεσοναντ/νον−ρεσοναντ mοδαλ χοντριβυτιονσ. Dεπενδινγ ον σιmπλιφψινγ κινεmατιχ mοδελινγ ανδ ασσιγνεδ σψστεm παραmετερσ, αππροξιmατε ηοριζονταλ/ινχλινεδ χαβλε mοδελσ αρε τηορουγηλψ ϖαλιδατεδ βψ νυmεριχαλλψ εϖαλυατινγ στατιχσ ανδ νον−πλαναρ/πλαναρ λινεαρ/νον−λινεαρ δψναmιχσ αγαινστ τηοσε οφ τηε εξαχτ mοδελ. Μορεοϖερ, τηε mοδαλ χουπλινγ ρολε ανδ χοντριβυτιον οφ σψστεm λονγιτυδιναλ δψναmιχσ αρε δισχυσσεδ φορ ηοριζονταλ χαβλεσ, σηοωινγ σοmε mεανινγφυλ εφφεχτσ δυε το κινεmατιχ χονδενσατιον.Κεψ ωορδσ: ηοριζονταλ/ινχλινεδ σαγγεδ χαβλε, εξαχτ/αππροξιmατε mοδελ, ιντερναλ ρεσονανχε, ηιγηερ−ορδερ εφφεχτσ, νον−λινεαρ φρεε ϖιβρατιον, λονγιτυδιναλ δψναmιχσ

show abstract

“…By means of the variational formulation, the governing exact PDEs of 3-D coupled undamped unforced motion of the cable about its static equilibrium read [20,21,31]:…”

Section: Exact Equations Of Motionmentioning

confidence: 99%

Section: Exact Equations Of Motionmentioning

confidence: 99%

Section: Steady-state Resonantly Coupled Motionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part I: Theoretical formulation and model validation

2006

Self Cite

View full text Add to dashboard Cite

show abstract

“…Considering just the in-plane response, [Lilien & Pinto Da Costa, 1994] showed that parametric excitation of modes is most significant when the ratio between the excitation frequency and the natural frequency of the cable is at or near 2 : 1. More generally, however, both in-plane and out-of-plane modes must be considered [Srinil et al, 2004]. For example, [Georgakis et al, 2001] considered multiple in-plane and out-of-plane modes for the case where auto-parametric resonance and cable nonlinearities are included.…”

Section: Introductionmentioning

confidence: 99%

Vibration Dynamics of an Inclined Cable Excited Near Its Second Natural Frequency

Tzanov

Krauskopf

Neild

2014

Int. J. Bifurcation Chaos

View full text Add to dashboard Cite

Inclined cables are essential structural elements that are used most prominently in cable stayed bridges. When the bridge deck oscillates due to an external force, such as passing traffic, cable vibrations can arise not only in the plane of excitation but also in the perpendicular plane. This undesirable phenomenon can be modelled as an auto-parametric resonance between the in-plane and out-of-plane modes of vibration of the cable. In this paper we consider a threemode model, capturing the second in-plane, and first and second out-of-plane modes, and use it to study the response of an inclined cable that is vertically excited at its lower (deck) support at a frequency close to the second natural frequency of the cable. Averaging is applied to the model and then the solutions and bifurcations of the resulting averaged differential equations are investigated and mapped out with numerical continuation. In this way, we present a detailed bifurcation study of the different possible responses of the cable. We first consider the equilibria of the averaged model, of which there are four types that are distinguished by whether each of the two out-of-plane modes is present or not in the cable response. Each type of equilibrium is computed and represented as a surface over the plane of amplitude and frequency of the forcing. The stability of the equilibria changes and different surfaces meet along curves of bifurcations, which are continued directly. Overall, we present a comprehensive geometric picture of the two-parameter bifurcation diagram of the constant-amplitude coupled-mode response of the cable. We then focused on bifurcating periodic orbits, which correspond to cable dynamics with varying amplitudes of the participating second in-plane and second out-of-plane modes. The range of excitation amplitude and frequency is determined where such whirling cable motion can occur. Further bifurcations -period-doubling cascades and a Shilnikov homoclinic bifurcation -are found that lead to a chaotic cable response. Whirling and chaotic cable dynamics are confirmed by time-step simulations of the full three-mode model. The different cable responses are characterized, and can be distinguished clearly, by the their motion at the quarter-span and by their frequency spectra.

show abstract

A robust and efficient numerical finite element method for cables

Bertrand

Acary

Lamarque

et al. 2020

Numerical Meth Engineering

View full text Add to dashboard Cite

Numerical simulation of cable systems remain delicate due to their geometrical non-linearity and also to their intrinsic unilateral constitutive law. Indeed Finite Element approaches (if not implemented carefully) fail to predict accurate equilibrium for cable structures. The major issue to be addressed is the ill-conditioning, starting configuration and wrong choice of descent direction during iterative methods. An iterative scheme based on Finite Element Method is presented to overcome this issue, even with large number of elements.

show abstract

Three-dimensional non-linear coupling and dynamic tension in the large-amplitude free vibrations of arbitrarily sagged cables

Cited by 74 publications

References 29 publications

Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part I: Theoretical formulation and model validation

Two-to-one resonant multi-modal dynamics of horizontal/inclined cables. Part I: Theoretical formulation and model validation

Vibration Dynamics of an Inclined Cable Excited Near Its Second Natural Frequency

A robust and efficient numerical finite element method for cables

Contact Info

Product

Resources

About