• Wind and Structures
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• v.4 no.4
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• pp.333-352
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• 2001

A two dimensional discrete vortex method (DIVEX) has been developed to predict unsteady and incompressible flow fields around closed bodies. The basis of the method is the discretisation of the vorticity field, rather than the velocity field, into a series of vortex particles that are free to move in the flow field that the particles collectively induce. This paper gives a brief description of the numerical implementation of DIVEX and presents the results of calculations on a recent suspension bridge deck section. The predictions for the static section demonstrate that the method captures the character of the flow field at different angles of incidence. In addition, flutter derivatives are obtained from simulations of the flow field around the section undergoing vertical and torsional oscillatory motion. The subsequent predictions of the critical flutter velocity compare well with those from both experiment and other computations. A brief study of the effect of flow control vanes on the aeroelastic stability of the bridge is also presented and the results from DIVEX are shown to be in accordance with previous analytical and experimental studies. In conclusion, the results indicate that DIVEX is a very useful design tool in the field of wind engineering.

• Wind and Structures
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• v.6 no.4
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• pp.263-278
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• 2003

This study investigates the effects of a bridge deck's width-to-depth (B/H) ratio and turbulence on buffeting response and flutter critical wind speed of long-span bridges by conducting section model tests. A streamlined box section and a plate girder section, each with four B/H ratios, were tested in smooth and turbulent flows. The results show that for the box girders, the response increases with the B/H ratio, especially in the vertical direction. For the plate girders, the vertical response also increases with the B/H ratio. However, the torsional response decreases as the B/H ratio increases. Increasing the B/H ratio and intensity of turbulence tends to improve the bridge's aerodynamic stability. Experimental results obtained from the section model tests agree reasonably with the calculated results obtained from a numerical analysis.

• Wind and Structures
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• v.18 no.3
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• pp.215-233
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• 2014

This paper presents a method to extract flutter derivatives of bridge decks based on a combination of the computational fluid dynamics (CFD), system simulations and system identifications. The incompressible solver adopts an Arbitrary Lagrangian-Eulerian (ALE) formulation with the finite volume discretization in space. The imposed sectional motion in heaving or pitching relies on exponential time series as input, with aerodynamic forces time histories acting on the section evaluated as output. System identifications are carried out to fit coefficients of the inputs and outputs of ARMA models, as to establish discrete-time aerodynamic models. System simulations of the established models are then performed as to obtain the lift and moment exerting on the sections to a sinusoidal displacement. It follows that flutter derivatives are identified. The present approaches are applied to a hexagon thin plate and a real bridge deck. The results are compared to the Theodorsen closed-form solution and those from wind tunnel tests. Satisfactory agreements are observed.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.26 no.5A
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• pp.887-899
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• 2006

The aim of this study is to investigate a correlation between fundamental data on aerodynamic characteristics of bridge girder cross-sections, such as aerodynamic force coefficients and flutter derivatives, and their aerodynamic behaviour. The section model tests were carried out in three stages. In the first stage, seven deck configurations were studied, namely; Six 2-edge girders and one box girder. In this stage, changes in aerodynamic force coefficients due to geometrical shape of girders, incidence angle of flow, wind directions and turbulence intensities were studied by static section model tests. In the second stage, the dynamic section model tests were carried out to investigate the relativity of static coefficients to dynamic responses. And finally, the two-dimensional (lift-torsion) aerodynamic derivatives of three bridge deck configurations were investigated by dynamic section model tests. The aerodynamic derivatives can be best described as a representation of the aerodynamic damping and the aerodynamic stiffness provided by the wind for a given deck geometry. The method employed here to extract these unsteady aerodynamic properties is known as the initial displacement technique. It involves the measurement of the decay in amplitude with time of an initial displacement of the deck in heave and torsion, for various wind speeds, in smooth flow. It is suggested that the proposed aerodynamic force coefficients and flutter derivatives of bridge girder sections will be potentially useful for the aeroelastic analysis and buffeting analysis.

• Wind and Structures
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• v.9 no.6
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• pp.441-455
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• 2006

A more applicable optimization model for extracting flutter derivatives of bridge decks is presented, which is suitable for time-varying weights for fitting errors and different lengths of vertical bending and torsional free vibration data. A stochastic search technique for searching the optimal solution of optimization problem is developed, which is more convenient in understanding and programming than the alternate iteration technique, and testified to be a valid and efficient method using two numerical examples. On the basis of the section model test of Sutong Bridge deck, the flutter derivatives are extracted by the stochastic search technique, and compared with the identification results using the modified least-square method. The Empirical Mode Decomposition method is employed to eliminate noise, trends and zero excursion of the collected free vibration data of vertical bending and torsional motion, by which the identification precision of flutter derivatives is improved.

• Wind and Structures
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• v.24 no.5
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• pp.481-500
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• 2017

A novel three-degree-of-freedom (DOF) forced vibration system has been developed for identification of aeroelastic (self-excited) load parameters used in time-domain response analysis of wind-excited flexible structures. This system is capable of forcing sinusoidal motions on a section model of a structure that is used in wind tunnel aeroelastic studies along all three degrees of freedom - along-wind, cross-wind, and torsional - simultaneously or in any combination thereof. It utilizes three linear actuators to force vibrations at a consistent frequency but varying amplitudes between the three. This system was designed to identify all the parameters, namely, aeroelastic- damping and stiffness that appear in self-excited (motion-dependent) load formulation either in time-domain (rational functions) or frequency-domain (flutter derivatives). Relatively large displacements (at low frequencies) can be generated by the system, if required. Results from three experiments, airfoil, streamlined bridge deck and a bluff-shaped bridge deck, are presented to demonstrate the functionality and robustness of the system and its applicability to multiple cross-section types. The system will allow routine identification of aeroelastic parameters through wind tunnel tests that can be used to predict response of flexible structures in extreme and transient wind conditions.

• Wind and Structures
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• v.28 no.4
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• pp.255-270
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• 2019

Aerodynamic configurations of bridge decks have significant effects on the aerostatic torsional divergence and flutter forsuper long-span bridges, which are onset for selection of suitable bridge decksfor those bridges. Based on a cable-stayed bridge with double main spans of 1500 m, considering typical twin-box, stiffening truss and closed-box section, which are the most commonly used form of bridge decks and assumed that the rigidity of those section is completely equivalent, are utilized to investigate the effects of aerodynamic configurations of bridge decks on aerodynamic instability performance comprised of the aerostatic torsional divergence and flutter, by means of wind tunnel tests and numerical calculations, including three-dimensional (3D) multimode flutter analysis and nonlinear aerostatic analysis. Regarding the aerostatic torsional divergence, the results obtained in this study show twin-box section is the best, closed-box section the second-best, and the stiffening truss section the worst. Regarding the flutter, the flutter stability of the twin-box section is far better than that of the stiffening truss and closed-box section. Furthermore, wind-resistance design depends on the torsional divergence for the twin-box and stiffening truss section. However, there are obvious competitive relationships between the aerostatic torsional divergence and flutter for the closed-box section. Flutter occur before aerostatic instability at initial attack angle of $+3^{\circ}$ and $0^{\circ}$, while the aerostatic torsional divergence occur before flutter at initial attack angle of $-3^{\circ}$. The twin-box section is the best in terms of both aerostatic and flutter stability among those bridge decks. Then mechanisms of aerostatic torsional divergence are revealed by tracking the cable forces synchronous with deformation of the bridge decksin the instability process. It was also found that the onset wind velocities of these bridge decks are very similar at attack angle of $-3^{\circ}$. This indicatesthat a stable triangular structure made up of the cable planes, the tower, and the bridge deck greatly improves the aerostatic stability of the structure, while the aerodynamic effects associated with the aerodynamic configurations of the bridge decks have little effects on the aerostatic stability at initial attack angle of $-3^{\circ}$. In addition, instability patterns of the bridge depend on both the initial attack angles and aerodynamic configurations of the bridge decks. This study is helpful in determining bridge decksfor super long-span bridges in future.

• Wind and Structures
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• v.10 no.5
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• pp.463-479
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• 2007

A series of wind tunnel sectional model dynamic tests of a twin-deck bridge were conducted at the CLP Power Wind/Wave Tunnel Facility (WWTF) of The Hong Kong University of Science and Technology (HKUST) to investigate the effects of gap-width on the self-excited vibrations and the dynamic and aerodynamic characteristics of the bridge. Five 2.9 m long models with different gap-widths were fabricated and suspended in the wind tunnel to simulate a two-degrees-of-freedom (2DOF) bridge dynamic system, free to vibrate in both vertical and torsional directions. The mass, vertical frequency, and the torsional-to-vertical frequency ratio of the 2DOF systems were fixed to emphasize the effects of gap-width. A free-vibration test methodology was employed and the Eigensystem Realization Algorithm (ERA) was utilized to extract the eight flutter derivatives and the modal parameters from the coupled free-decay responses. The results of the zero gap-width configuration were in reasonable agreement with the theoretical values for an ideal thin flat plate in smooth flow and the published results of models with similar cross-sections, thus validating the experimental and analytical techniques utilized in this study. The methodology was further verified by the comparison between the measured and predicted free-decay responses. A comparison of results for different gap-widths revealed that variations of the gap-width mainly affect the torsional damping property, and that the configurations with greater gap-widths show a higher torsional damping ratio and hence stronger aerodynamic stability of the bridge.

• Wind and Structures
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• v.6 no.3
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• pp.179-196
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• 2003

A long suspension bridge is often located within a unique wind environment, and strong winds at the site seldom attack the bridge at a right angle to its long axis. This paper thus investigates the buffeting response of long suspension bridges to skew winds. The conventional buffeting analysis in the frequency domain is first improved to take into account skew winds based on the quasi-steady theory and the oblique strip theory in conjunction with the finite element method and the pseudo-excitation method. The aerodynamic coefficients and flutter derivatives of the Tsing Ma suspension bridge deck under skew winds, which are required in the improved buffeting analysis, are then measured in a wind tunnel using specially designed test rigs. The field measurement data, which were recorded during Typhoon Sam in 1999 by the Wind And Structural Health Monitoring System (WASHMS) installed on the Tsing Ma Bridge, are analyzed to obtain both wind characteristics and buffeting responses. Finally, the field measured buffeting responses of the Tsing Ma Bridge are compared with those from the computer simulation using the improved method and the aerodynamic coefficients and flutter derivatives measured under skew winds. The comparison is found satisfactory in general.

• Wind and Structures
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• v.16 no.6
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• pp.561-577
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• 2013

Rational Functions are used to express the self-excited aerodynamic forces acting on a flexible structure for use in time-domain flutter analysis. The Rational Function Approximation (RFA) approach involves obtaining of these Rational Functions from the frequency-dependent flutter derivatives by using an approximation. In the past, an algorithm was developed to directly extract these Rational Functions from wind tunnel section model tests in free vibration. In this paper, an algorithm is presented for direct extraction of these Rational Functions from section model tests in forced vibration. The motivation for using forced-vibration method came from the potential use of these Rational Functions to predict aerodynamic loads and response of flexible structures at high wind speeds and in turbulent wind environment. Numerical tests were performed to verify the robustness and performance of the algorithm under different noise levels that are expected in wind tunnel data. Wind tunnel tests in one degree-of-freedom (vertical/torsional) forced vibration were performed on a streamlined bridge deck section model whose Rational Functions were compared with those obtained by free vibration for the same model.