• Wind and Structures
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• v.31 no.5
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• pp.403-418
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• 2020

To investigate the effects of central buckles on the dynamic behavior and flutter stability of long-span suspension bridges, four different connection options between the main cable and the girder near the mid-span position of the Aizhai Bridge were studied. Based on the flutter derivatives obtained from wind tunnel tests, formulations of self-excited forces in the time domain were obtained using a nonlinear least square fitting method and a time-domain flutter analysis was realized. Subsequently, the influences of the central buckles on the critical flutter velocity, flutter frequency, and three-dimensional flutter states of the bridge were investigated. The results show that the central buckles can significantly increase the frequency of the longitudinal floating mode of the bridge and have greater influence on the frequencies of the asymmetric lateral bending mode and asymmetric torsion mode than on that of the symmetric ones. As such, the central buckles have small impact on the critical flutter velocity due to that the flutter mode of the Aizhai Bridge was essentially the symmetric torsion mode coupled with the symmetric vertical mode. However, the central buckles have certain impact on the flutter mode and the three-dimensional flutter states of the bridge. In addition, it is found that the phenomenon of complex beat vibrations (called intermittent flutter phenomenon) appeared in the flutter state of the bridge when the structural damping is 0 or very low.

• Wind and Structures
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• v.7 no.3
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• pp.187-202
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• 2004

Wind tunnel experiments are often performed for the identification of aeroelastic parameters known as flutter derivatives that are necessary for the prediction of flutter instability for flexible structures. Experimental determination of all the eighteen flutter derivatives for a section model facilitates complete understanding of the physical mechanism of flutter. However, work in the field of identifying all the eighteen flutter derivatives using section models with all three degree-of-freedom (DOF) has been limited. In the current paper, all eighteen flutter derivatives for a streamlined bridge deck and an airfoil section model were identified by using a new system identification technique, namely, Iterative Least Squares (ILS) approach. Flutter derivatives of the current bridge and the Tsurumi bridge are compared. Flutter derivatives related to the lateral DOF have been emphasized. Pseudo-steady theory for predicting some of the flutter derivatives is verified by comparing with experimental data. The three-DOF suspension system and the electromagnetic system for providing the initial conditions for free-vibration of the section model are also discussed.

• Wind and Structures
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• v.25 no.4
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• pp.343-360
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• 2017

The post-flutter state of streamlined steel box girder is studied in this paper. Firstly, the nonlinear aerodynamic self-excited forces of the bridge deck cross section were investigated by CFD dynamic mesh technique and then the nonlinear flutter derivatives were identified on this basis. Secondly, based on the 2-degree-of-freedom (DOF) coupling flutter theory, the torsional amplitude and the nonlinear flutter derivatives were introduced into the traditional direct flutter calculation method, and the original program was improved to the "post-flutter state analysis program" so that it can predict not only the critical flutter velocity but also the movement of the girder in the post-flutter state. Finally, wind tunnel tests were set to verify the method proposed in this paper. The results show that the effect of vertical amplitude on the nonlinear flutter derivatives is negligible, but the torsional amplitude is not; with the increase of wind speed, the post-flutter state of streamlined steel box girder includes four stages, namely, "little amplitude zone", "step amplitude zone", "linearly growing amplitude zone" and "divergence zone"; damping ratio has limited effect on the critical flutter velocity and the steady state response in the post-flutter state; after flutter occurs, the vibration form is a single frequency vibration coupled with torsional and vertical DOF.

• International Journal of Aeronautical and Space Sciences
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• v.7 no.2
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• pp.70-85
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• 2006

The supersonic flutter suppression of a cantilevered plate wing is studied with the finite element method and the quasi-steady aerodynamic theory. We suppress wing flutter by using piezoelectric materials and electric devices. Two approaches to flutter suppression using piezoelectric materials are presented; an energy-recycling semi-active approach and a negative capacitance approach. To assess their flutter suppression performances, we simulate flutter dynamics of the plate wing to which piezoelectric patches are attached. The critical dynamic pressure drastically increases with our flutter control using a negative capacitor.

• Wind and Structures
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• v.27 no.3
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• pp.175-186
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• 2018

With the continuous increase of span lengths, modern bridges are becoming much more flexible and more prone to flutter under wind excitations. A reasonable probabilistic flutter analysis of long-span bridges involving random and uncertain variables may have to be taken into consideration. This paper presents a method for estimating the reliability index and failure probability due to flutter, which considers the very important variables including the extreme wind velocity at bridge site, damping ratio, mathematical modeling, and flutter derivatives. The Aizhai Bridge in China is selected as an example to demonstrate the numerical procedure for the flutter reliability analysis. In the presented method, the joint probability density function of wind speed and wind direction at the deck level of the bridge is first established. Then, based on the fundamental theories of structural reliability, the reliability index and failure probability due to flutter of the Aizhai Bridge is investigated by applying the Monte Carlo method and the first order reliability method (FORM). The probabilistic flutter analysis can provide a guideline in the design of long-span bridges and the results show that the structural damping and flutter derivatives have significant effects on the flutter reliability, more accurate and reliable data of which is needed.

• Wind and Structures
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• v.17 no.3
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• pp.275-298
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• 2013

This paper presents a number of approximated analytical formulations for the flutter analysis of long-span bridges using the so-called uncoupled flutter derivatives. The formulae have been developed from the simplified framework of a bimodal coupled flutter problem. As a result, the proposed method represents an extension of Selberg's empirical formula to generic bridge sections, which may be prone to one of the aeroelastic instability such as coupled-mode or single-mode (either dominated by torsion or heaving mode) flutter. Two approximated expressions for the flutter derivatives are required so that only the experimental flutter derivatives of ($H_1^*$, $A_2^*$) are measured to calculate the onset flutter. Based on asymptotic expansions of the flutter derivatives, a further simplified formula was derived to predict the critical wind speed of the cross section, which is prone to the coupled-mode flutter at large reduced wind speeds. The numerical results produced by the proposed formulas have been compared with results obtained by complex eigenvalue analysis and available approximated methods show that they seem to give satisfactory results for a wide range of study cases. Thus, these formulas can be used in the assessment of bridge flutter performance at the preliminary design stage.

• Wind and Structures
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• v.11 no.3
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• pp.209-220
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• 2008

Flutter derivatives provide the basis of predicting the critical wind speed in flutter and buffeting analysis of long-span cable-supported bridges. Many studies have been performed on the methods and applications of identification of flutter derivatives of bridge decks under wind action. In fact, strong wind, especially typhoon, is always accompanied by heavy rain. Then, what is the effect of rain on flutter derivatives and flutter critical wind speed of bridges? Unfortunately, there have been no studies on this subject. This paper makes an initial study on this problem. Covariance-driven Stochastic Subspace Identification (SSI in short) which is capable of estimating the flutter derivatives of bridge decks from their steady random responses is presented first. An experimental set-up is specially designed and manufactured to produce the conditions of rain and wind. Wind tunnel tests of a quasi-streamlined thin plate model are conducted under conditions of only wind action and simultaneous wind-rain action, respectively. The flutter derivatives are then extracted by the SSI method, and comparisons are made between the flutter derivatives under the two different conditions. The comparison results tentatively indicate that rain has non-trivial effects on flutter derivatives, especially on and $H_2$ and $A_2$thus the flutter critical wind speeds of bridges.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.4
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• pp.393-400
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• 2012

This paper deals with a development of 2-DOF flutter experiment equipment which represents a 2-DOF typical section model. For a conventional 2-DOF flutter experiment equipment, it is hard to observe flutter boundary clearly due to the complexity of the experiment equipment. To refine our flutter experiment equipment system, a compliant mechanism based torsional spring is used. Well-designed extruded aluminum pipe works as a torsional spring. SolidWorks and ANSYS are used for modeling, analysis and design of the torsional spring. With this designed torsional spring, the 2-DOF flutter experiment equipment is developed and wind tunnel tests are performed. Clear flutter boundary which is estimated by classical flutter analysis is observed in the experiments.

• Wind and Structures
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• v.15 no.3
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• pp.209-221
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• 2012

The flutter reliability analysis of long span bridges requires use of a software tool that predicts the uncertainty in a flutter response due to uncertainties in the model formulation and input parameters. Existing flutter analysis numerical codes are not capable of dealing with stochastic uncertainty in the analysis of long span bridges. The goal of the present work is to develop a software tool (FREASB) to enable designers to efficiently and accurately conduct flutter reliability analysis of long span bridges. The FREASB interfaces an open-source Matlab toolbox for structural reliability analysis (FERUM) with a typical deterministic flutter analysis code. The paper presents a brief introduction to the generalized first-order reliability method implemented in FREASB and key steps involved in coupling it with a typical deterministic flutter analysis code. A numerical example concerning flutter reliability analysis of a long span suspension bridge with a main span of 1385 m is presented to demonstrate the application and effectiveness of the methodology and the software.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2012.04a
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• pp.429-434
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• 2012

This paper deals with a development of 2-DOF flutter experiment equipment which represents a 2-DOF typical section model. For a conventional 2-DOF flutter experiment equipment, it is hard to observe flutter boundary clearly due to the complexity of the experiment equipment. To refine our flutter experiment equipment system, a compliant mechanism based torsional spring is used. Well-designed extruded aluminum pipe works as a torsional spring. SolidWorks and ANSYS are used for modeling, analysis and design of the torsional spring. With this designed torsional spring, the 2-DOF flutter experiment equipment is developed and wind tunnel tests are performed. Clear flutter boundary which is estimated by classical flutter analysis is observed in the experiments.