The buffeting wind loading of structural members at an arbitrary attitude in the flow

Strømmen, Einar N.; Hjorth-Hansen, Erik

doi:10.1016/0167-6105(94)00092-r

Cited by 23 publications

(4 citation statements)

References 4 publications

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“…The most popular model adopted for the structure is the unbounded rigid cylinder; however, the iced cable problem adds further difficulties, due to the curvature of its centerline and the random variation of the section. To tentatively tackle the problem, a simple model is adopted here, by introducing the following assumptions: (a) quasisteady theory [Blevins 1990] is believed applicable, according to which the loads acting on the moving body at a certain instant are identical to those exerted on the body at rest in the same position; (b) the curvature of the cable is negligibly small; (c) loads are evaluated in the current configuration Ꮿ, by accounting for the twist angle ϑ, but neglecting the smaller flexural rotations ϑ 2,3 = ᏻ (ϑδ) (remember Equations (2) and (13) 2 ), which, according to the so-called cosine rule [Strømmen and Hjorth-Hansen 1995], have small influence; (d) the ice is assumed to be uniformly distributed along the cable, consistently with the hypothesis of planar reference configuration; (e) aerodynamic couples are neglected.…”

Section: Aerodynamic Forcesmentioning

confidence: 99%

A linear curved-beam model for the analysis of galloping in suspended cables

Luongo

Zulli

Piccardo

2007

JOMMS

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A linear model of curved, prestressed, no-shear, elastic beam, loaded by wind forces, is formulated. The beam is assumed to be planar in its reference configuration, under its own weight and static wind forces. The incremental equilibrium equations around the prestressed state are derived, in which shear forces are condensed. By using a linear elastic constitutive law and accounting for damping and inertial effects, the complete equations of motion are obtained. They are then greatly simplified by estimating the order of magnitude of all their terms, under the hypotheses of small sag-to-span ratio, order-1 aspect ratio of the (compact) section, characteristic section radius much smaller than length (slender cable), small transversal-to-longitudinal and transversal-to-torsional wave velocity ratios. A system of two integrodifferential equations is drawn in the two transversal displacements only. A simplified model of aerodynamic forces is then developed according to a quasisteady formulation. The nonlinear, nontrivial equilibrium path of the cable subjected to increasing static wind forces is successively evaluated, and the influence of the angle of twist on the equilibrium is discussed. Then stability is studied by discretizing the equations of motion via a Galerkin approach and analyzing the small oscillations around the nontrivial equilibrium. Finally, the role of the angle of twist on the dynamic stability of the cable is discussed for some sample cables.

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Section: Aerodynamic Forcesmentioning

confidence: 99%

A linear curved-beam model for the analysis of galloping in suspended cables

Luongo

Zulli

Piccardo

2007

JOMMS

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“…(9)) then agrees with the equivalent terms in the formulation of Strømmen and Hjorth-Hansen (1995). 1 For the special case of a ¼ 0, e.g.…”

Section: Aerodynamic Damping Matrix Per Unit Length For Coupled 2domentioning

confidence: 56%

“…However, a complete theoretical model of the behaviour has been lacking, since galloping analysis normally treats the force coefficients as invariant with Reynolds number and considers only the component of flow velocity normal to the cable to be effective (Skarecky, 1975). Strømmen and Hjorth-Hansen (1995) have dealt with the three-dimensional geometry for buffeting of members at an arbitrary attitude to the flow. Their formulation includes the full quasi-steady aerodynamic damping matrix, but assumes that the force coefficients with respect to the normal component of the flow only vary with the ''vertical'' angle of attack.…”

Section: Article In Pressmentioning

confidence: 99%

Two-degree-of-freedom inclined cable galloping—Part 1: General formulation and solution for perfectly tuned system

Macdonald

Larose

2008

Journal of Wind Engineering and Industrial Aerodynamics

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“…(11) is a generalised version of the aerodynamic damping matrix proposed by Piccardo (1993), allowing not only for arbitrary orientation of the principal axes but also for arbitrary location of the aerodynamic centre. The top left 2 Â 2 submatrix of C a is identical to the aerodynamic damping matrix for 2DOF translational galloping presented by Nikitas and Macdonald (2014) or a simplified version of the ones given by Strømmen and Hjorth-Hansen (1995), Macdonald and Larose (2008a) and Piccardo et al (2011), who all allowed for a skew angle in the third dimension. The other elements of C a are found to agree with the equivalent equations given by Gjelstrup and Georgakis (2011) (except for an apparent transcription error for their ∂Fy ∂ _ θ ), after substitution of certain angle variables and neglecting the terms allowing for the differentials with respect to Reynolds number and skew angle.…”

Section: Derivation Of the 3dof Aerodynamic Damping Matrixmentioning

confidence: 99%

An analytical solution for the galloping stability of a 3 degree-of-freedom system based on quasi-steady theory

Macdonald

2016

Journal of Fluids and Structures

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms An analytical solution for the galloping stability of a 3 degree-of-freedom system based on quasi-steady theory a b s t r a c tThe aerodynamic forces on a two-dimensional three-degree-of-freedom (3DOF-heave, sway and torsion) body of arbitrary cross-section are considered, for arbitrary wind direction relative to the principal structural axes. The full 3DOF aerodynamic damping matrix is derived, based on quasi-steady theory, using the commonly-used concept of an aerodynamic centre to represent the effect of the torsional velocity on the aerodynamic forces. The aerodynamic coefficients are assumed to be consistent functions of only the relative angle of attack. It is shown that the determinant of the quasi-steady aerodynamic damping matrix is always zero. The galloping stability of the aerodynamically coupled system is then addressed by formulating the eigenvalue problem, for which analytical solutions are derived for the case of perfectly tuned structural natural frequencies. The solutions define a non-dimensional effective aerodynamic damping coefficient, indicating how stable the system is. A trivial solution always exists, with zero effective aerodynamic damping, corresponding to rotation about the aerodynamic centre, and relatively simple exact closed-form solutions are derived for the other one or two solutions, the minimum solution defining the stability of the system. Example results are presented and discussed for square, rectangular (aspect ratio 3) and equilateral triangular sections and a lightly iced cable, and they are compared with results using previous solutions for 2DOF translational and 1DOF pure torsional galloping. For the shapes considered it is found that the stability of the 3DOF system is normally close to that of the 2DOF translational system, with a relatively small influence of the stability of the torsional degree of freedom, although in some instances, especially at the critical angles of attack, it can significantly affect the stability.

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The buffeting wind loading of structural members at an arbitrary attitude in the flow

Cited by 23 publications

References 4 publications

A linear curved-beam model for the analysis of galloping in suspended cables

A linear curved-beam model for the analysis of galloping in suspended cables

Two-degree-of-freedom inclined cable galloping—Part 1: General formulation and solution for perfectly tuned system

An analytical solution for the galloping stability of a 3 degree-of-freedom system based on quasi-steady theory

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