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Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Agrivoltaics is a relatively new term used originally for integrating photovoltaic (PV) systems into the agricultural landscape and expanded to applications such as animal farms, greenhouses, and recreational parks. The dual use of land offers multiple solutions for the renewable energy sector worldwide, provided it can be implemented without negatively impacting agricultural production. However, agrivoltaics represent a relatively new technology, facing challenges including economic viability, vulnerability to wind loads, and interference with growing crops. This paper reviews the recent research on integrating agrivoltaics with farming applications, focusing on challenges, wind impact on agrivoltaics, and economic solutions. The effect of agrivoltaics on temperature control of the lands is a critical factor in managing (1) water and the soil of the land, (2) animal comfort, and (3) greenhouse productivity, positively or negatively. In this review, a contradiction between the different versions of the American Society of Civil Engineers (ASCE) standards and the wind tunnel results is shown. Important factors affecting the wind load, such as damping and mass increase, optimum stow position, and aerodynamic edge modification, are highlighted with emphasis on the significant knowledge gap in the wind load mitigation methods. [ABSTRACT FROM AUTHOR]

Signal complexity analysis based entropy measure has been used to propose a model-free approach towards assessment of flutter critical wind speed and identification of the type of flutter in wind tunnel testing of long span bridges. The approach is based only on the measured output responses from the structure, which accounts for appropriate effects that stem from the non-linearity of the structure and fluid structure interaction. The usefulness of the proposed approach has been demonstrated with dynamic sectional models of two deck cross-sections in wind tunnel. The gain in regularity of responses on approaching the flutter critical wind speed, demonstrated with time history of responses and recurrence quantification plots, has been quantified using sample entropy. Based on the sensitivity of the sample entropy values on the embedding dimension, it has been suggested to adopt embedding dimension in the range of 2 and 5, to obtain a swift estimate of the state of the dynamic system. The proposed approach has shown potential to provide valuable insight about the flutter instability and distinguish between different types of flutter without requiring prior knowledge about the system under consideration. The study offers a promising complementary methodology to the conventional model-based approaches for evaluating flutter critical wind speed. [ABSTRACT FROM AUTHOR]

In this paper, the critical wind speed of flutter has been predicted by using two-dimensional computational fluid dynamics (CFD) model side by side with the empirical formula (Selberg's formula, 1961). The deck section of the Great Belt Bridge's main span has been used herein as a reference among other sectional varieties. For each case of the examined sections, the width was changed case by case, while its depth maintained unchanged. Both of the two methods, the semi-empirical using the "CFD" simulation and the empirical formula have been employed to predict the critical wind speed of flutter for a variety of the (width/depth) ratio and the natural frequency ratio (torsional/vertical). The results were obtained from the semi-empirical method and validated by comparison with wind tunnel test for typical section model of the Great Belt Bridge presented in the literature, and also compared with the empirical method. The results were represented graphically for each method and they have indicated the variation of the critical speed in terms of the section dimension and its natural frequencies, and furthermore, the change of the difference between the two methods was represented too. [ABSTRACT FROM AUTHOR]

This study presents a comprehensive investigation on the characteristics of the aerodynamic damping and amplitude-dependent flutter derivatives of a streamlined box girder for various wind angles of attack through a scaled section-model free vibration wind tunnel test. The response characteristics of the section model in vertical, torsional, and vertical–torsional coupled directions are investigated. A piecewise sliding windows fitting method, which is effective, generic, and at the same time provides an accurate estimation of the amplitude-dependent damping ratio, is proposed. The method is applied in three experimental measured examples, and the yielded results match satisfactorily with the measurements, confirming the feasibility and the advantage of the proposed method. Besides, the modal damping ratios of the section model for the considered degrees of freedom at different cases are identified from the method. The evolution of the aerodynamic damping with the wind speed and wind angle of attack and its influence on the generation of stable and unstable limit cycle oscillations and flutter response are discussed. The contribution of vertical and torsional motion to the generation of different flutter types is revealed. The full set of amplitude-dependent flutter derivatives is identified from the experimental modal properties of the different dynamic systems. The accuracy of the flutter derivatives is cross-validated through a free vibration wind tunnel test. [ABSTRACT FROM AUTHOR]

Featured Application: This study provides a simplified approach to the flutter analysis of suspension bridges having two superposed decks. The George Washington Bridge engineering case is analyzed, in consideration of its historical relevance and age. The obtained results are compared with the predictions of simplified formulations available from other sources. We deal with the flutter analysis of the George Washington bridge, in both the single- and double-deck configurations of 1931 and 1962, respectively. The influence of the additional lower deck on the aerodynamic behavior is investigated. To overcome the lack of aerodynamic data, a simplified approach is followed based on Fung's formulation, in which the flutter derivatives are expressed in terms of the real and imaginary parts of the Theodorsen function and of the steady-state aerodynamic coefficients of the deck cross-section. The latter are obtained by Computational Fluid Dynamics simulations conducted in ANSYS FLUENT, whereas the ANSYS Mechanical APDL finite element package is used to perform the flutter analyses. Two different methods for the application of the aeroelastic forces are employed for the double-deck configuration: (i) self-excited forces, based on flutter derivatives related to the whole cross-section, acting on the upper deck; and (ii) self-excited forces, based on flutter derivatives related to the single deck, simultaneously applied to the upper and lower decks. The obtained results are critically compared with theoretical predictions of simple formulas available from the literature; it is suggested that laboratory tests are needed since no experimental results seem to be available. [ABSTRACT FROM AUTHOR]

The significance of long-span bridges being susceptible to wind-induced vibrations and the need for evaluating their aerodynamic performance is the focus of this study. The main emphasis is on experimental methods for assessing the bridges' aerodynamic stability, using sectional model tests with the free vibration technique. The dynamic properties of the model are determined from the measured response, using various system identification methods, including the modified Ibrahim time domain (MITD) and iterative least squares (ILS) for two-degree-of-freedom systems and the logarithmic decrement method (LDM) and the Hilbert transform method (HTM) for single-degree-of-freedom (SDOF) systems. A new dynamic testing setup was designed to facilitate single-degree-of-freedom (heave and pitch) and coupled two-degree-of-freedom (2DOF) motion in a wind tunnel section model. The vertical and torsional stiffnesses of the model were adjusted with elastic springs. A Great Belt Bridge section model was selected for testing due to its streamlined aerodynamic shape. The direct and crossflow derivatives were extracted from the measured response using the system identification methods mentioned. Additionally, analytical studies and numerical computational fluid dynamics simulations were conducted to validate the experimental results. The study found that HTM is most effective in SDOF due to its ability to extract both damping and frequency from the nonlinear response, whereas the MITD method is faster in converging system parameters in 2DOF system tests. The experimental and numerical results are comparable to the flat plate, which confirms the streamlined behavior of the Great Belt section from an aerodynamic perspective. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Vertical stabilizers have been proved to be effective for flutter suppression of long-span bridges, while their self-stability under strong winds should be taken seriously. This study takes a steel truss stiffening girder as an example, and effects of oblique stabilizers on the flutter performance are investigated. After discussing the wind environment above the bridge site, the flutter derivatives of girder extracted by numerical simulations are given to compute the critical flutter wind speed by a bimodal coupled flutter analysis method. Subsequently, with considering the lateral self-excited force, the flutter performance is accurately evaluated by performing complex modal characteristics based on a full-order modal flutter analysis method. After setting different types of stabilizers with different covering lengths, improvement of the flutter performance is discussed. The results show that the flutter performance is related to multiple modes. Temporary flutter instability of a modal branch may be caused due to the curve-veering phenomenon among similar modes. Thus, the critical flutter wind speed may be overestimated by bimodal-coupled flutter analyses. At negative angles of attack, the set of oblique stabilizers are flutter favorable by improving the temporary flutter instability. Setting partial stabilizers around the mid-span is more flutter favorable than covering the entire girder. • The flutter stability of bridge is related to multiple modes with similar characteristics. • The lateral self-excited force providing positive modal damping should be considered. • Temporary flutter instability of a modal branch is caused by the curve veering. • Setting the oblique stabilizers improves the temporary flutter instability. • Setting partial stabilizers around the mid-span is more flutter favorable. [ABSTRACT FROM AUTHOR]

Composite materials enable the tailoring of load-dependent, passive, shape adaptation because of the directional stiffness of the fibers. However, excessive flow-induced vibrations and dynamic instabilities represent a design challenge for composite marine appendages. We develop DCFoil, a dynamic composite foil solver that uses one-dimensional models—composite beam elements and unsteady lifting line theory—to perform static and dynamic frequency domain analysis. The program is differentiated to provide derivatives of an aggregated flutter function with respect to design variables. The flutter function characterizes dynamic hydroelastic stability. We apply the solver to investigate the hydroelastic performance of a composite fin bulb keel based on the IMOCA 60 class of racing yachts, which were reported to have flutter problems. Based on the derivatives computed for this bulb keel, we found that the foil thickness has the most significant impact on flutter speed. This work shows both the development of and utility of a program with flutter derivatives for flexible composite marine appendage design. [ABSTRACT FROM AUTHOR]

The shape design and optimization of bluff decks prone to aeroelastic phenomena require emulating the fluid-structure interaction parameters as a function of the body shape and the oscillation frequency. This is particularly relevant for long- and medium-span bridges equipped with single-box decks that are far from being considered streamlined and for other girder typologies such as traditional truss decks and modern twin- and multi-box decks. The success of aero-structural design frameworks, which are inherently iterative, relies on the efficient and accurate numerical evaluation of the wind-induced responses. This study proposes emulating the fluid-structure interaction parameters of bluff decks using surrogate modeling techniques to integrate them into aero-structural optimization frameworks. The surrogate is trained with data extracted from forced-vibration CFD simulations of a typical single-box girder to emulate the values of the flutter derivatives as a function of the deck shape and reduced velocity. The focus is on deck configurations ranging from streamlined to bluff cross-sections and on low reduced velocities to capture eventual aerodynamic nonlinearities. The girder cross-section geometry is tailored based on its buffeting performance. This design tool is fundamental to finding the optimum balance between the structural and aeroelastic requirements that drive the design of bluff deck bridges. • A computational method for the aero-structural design of bluff decks is proposed. • An aeroelastic emulator enables deck shape variations including bluff geometries. • CFD simulations of force vibrations are used to extract the 18 flutter derivatives. • The sampling plan focuses on low reduced velocities to capture nonlinear aerodynamics. • A buffeting-resistant deck shape tailoring shows the performance of the methodology. [ABSTRACT FROM AUTHOR]

We deal with the flutter analysis of the George Washington bridge, in both the single- and double-deck configurations of 1931 and 1962, respectively. The influence of the additional lower deck on the aerodynamic behavior is investigated. To overcome the lack of aerodynamic data, a simplified approach is followed based on Fung’s formulation, in which the flutter derivatives are expressed in terms of the real and imaginary parts of the Theodorsen function and of the steady-state aerodynamic coefficients of the deck cross-section. The latter are obtained by Computational Fluid Dynamics simulations conducted in ANSYS FLUENT, whereas the ANSYS Mechanical APDL finite element package is used to perform the flutter analyses. Two different methods for the application of the aeroelastic forces are employed for the double-deck configuration: (i) self-excited forces, based on flutter derivatives related to the whole cross-section, acting on the upper deck; and (ii) self-excited forces, based on flutter derivatives related to the single deck, simultaneously applied to the upper and lower decks. The obtained results are critically compared with theoretical predictions of simple formulas available from the literature; it is suggested that laboratory tests are needed since no experimental results seem to be available.

The significance of long-span bridges being susceptible to wind-induced vibrations and the need for evaluating their aerodynamic performance is the focus of this study. The main emphasis is on experimental methods for assessing the bridges’ aerodynamic stability, using sectional model tests with the free vibration technique. The dynamic properties of the model are determined from the measured response, using various system identification methods, including the modified Ibrahim time domain (MITD) and iterative least squares (ILS) for two-degree-of-freedom systems and the logarithmic decrement method (LDM) and the Hilbert transform method (HTM) for single-degree-of-freedom (SDOF) systems. A new dynamic testing setup was designed to facilitate single-degree-of-freedom (heave and pitch) and coupled two-degree-of-freedom (2DOF) motion in a wind tunnel section model. The vertical and torsional stiffnesses of the model were adjusted with elastic springs. A Great Belt Bridge section model was selected for testing due to its streamlined aerodynamic shape. The direct and crossflow derivatives were extracted from the measured response using the system identification methods mentioned. Additionally, analytical studies and numerical computational fluid dynamics simulations were conducted to validate the experimental results. The study found that HTM is most effective in SDOF due to its ability to extract both damping and frequency from the nonlinear response, whereas the MITD method is faster in converging system parameters in 2DOF system tests. The experimental and numerical results are comparable to the flat plate, which confirms the streamlined behavior of the Great Belt section from an aerodynamic perspective.

The clarification of the nonlinear and unsteady aerodynamic characteristics of a quasi-flat plate is of great importance to predict its wind-induced post-flutter behavior. Forced motion wind tunnel tests on a quasi-flat plate sectional model with a width-over-thickness ratio of 62.5:1 are conducted using the synchronous measurement of the dynamic forces and torsional displacements at various initial angles of attack (AoAs), vibration amplitudes and incoming wind speeds. The flutter derivatives related to torsional degree of freedom (DOF) are identified and compared. The nonlinear and unsteady characteristics of self-excited forces (SEFs) in terms of the frequency components and phase lag between the force and motion are quantitatively examined. The wind-induced energy maps of the quasi-flat plate at various initial AoAs are analyzed by introducing the aerodynamic work done by the self-excited lifting moment. A polynomial model is proposed to describe the nonlinear characteristics of the SEFs. It is validated that the flutter derivatives related to the torsional DOF are almost a single-valued function with respect to the reduced frequency, even at large vibration amplitudes. At large initial AoAs and oscillation amplitudes, the high-order frequency components of SEFs are significant, and the nonlinearity of the self-excited lifting moment is stronger than that of the self-excited lift force for torsional motion. This provides a reasonable explanation for the significant amplitude dependence of the flutter derivatives related to the lifting moment. The proposed polynomial nonlinear SEF model can achieve satisfactory accuracy in reproducing the SEFs in both time and frequency domains. [ABSTRACT FROM AUTHOR]

This paper presents a novel parameter identification and uncertainty quantification method for flutter derivatives estimation of bridge decks. The proposed approach is based on free-decay vibration records of a sectional model in wind tunnel tests, which consists of parameter identification by a heuristic optimization algorithm in the sense of weighted least squares and uncertainty quantification by a bootstrap technique. The novel contributions of the method are on three fronts. Firstly, weighting factors associated with vertical and torsional motion in the objective function are determined more reasonably using an iterative procedure rather than preassigned. Secondly, flutter derivatives are identified using a hybrid heuristic and classical optimization method, which integrates a modified artificial bee colony algorithm with the Powell's algorithm. Thirdly, a statistical bootstrap technique is used to quantify the uncertainties of flutter derivatives. The advantages of the proposed method with respect to other methods are faster and more accurate achievement of the global optimum, and refined uncertainty quantification in the identified flutter derivatives. The effectiveness and reliability of the proposed method are validated through noisy data of a numerically simulated thin plate and experimental data of a bridge deck sectional model. [ABSTRACT FROM AUTHOR]

Different engineering structures, e.g., long-span bridges, bundled conductors, and cable-supported photovoltaic modules, exhibit various frequency relationships among different degrees of freedom (DOFs). Despite extensive research, the initiation mechanisms of flutter remain somewhat ambiguous for a 3-DOF system considering heaving-lateral-torsional motions, especially when frequencies are close among different DOFs. This study introduced an explicit eigenvalue solution framework for tackling the 3-DOF linear flutter problem by utilizing matrix perturbation methods, enabling the extraction of modal damping and frequency solutions for all possible frequency scenarios. These solutions explicitly clarified the influence mechanism of all flutter derivatives (aerodynamic damping and stiffness), structural frequencies, and mechanical dampings. Important flutter derivatives, flutter risk level, and sensitivity level to mechanical damping and to frequency detuning were summarized in a table for all frequency scenarios, providing a panoramic perspective on flutter instability and the coupling mechanism. Numerical studies were conducted on a thin plate, the Akashi Kaikyo Bridge, and an eight-bundled conductor to examine the proposed explicit solutions. The results showed that approaching frequencies can amplify the coupling effect among different DOFs by half an order, but this does not necessarily mean the system is more prone to flutter. A system where the torsional frequency approximates the heaving/lateral frequency is expected to face a higher flutter risk if given significant torsional-related aerodynamic stiffness (H 3 * , P 3 *). Evidently, this high risk exhibits insensitivity to mechanical damping and small frequency-detuning. Though usually ignored in bridge flutter analysis, drag force and lateral motion could exert noticeable influence in a minority of cases, e.g., more than 10 m/s decrease of critical wind speed for the Akashi Kaikyo Bridge at large angles of attack. The proposed explicit solution framework provides a systematic view and new insights into the flutter initiation mechanism, serving as a reference in the design and studies of various engineering structures with different frequencies and coupling features. • Explicit solutions for modal damping and frequency are provided for 3-DOF linear flutter. • For all frequency scenarios, flutter initiation mechanism and coupling effect are revealed and compared. • Influence mechanism of all flutter derivatives and structural parameters are clarified. • Flutter risk and sensitivity level are summarized, providing design guidance for various structures. • Drag force and lateral motion could be important for bridge flutter at large attack angles. [ABSTRACT FROM AUTHOR]

This paper presents a novel parameter identification and uncertainty quantification method for flutter derivatives estimation of bridge decks. The proposed approach is based on free-decay vibration records of a sectional model in wind tunnel tests, which consists of parameter identification by a heuristic optimization algorithm in the sense of weighted least squares and uncertainty quantification by a bootstrap technique. The novel contributions of the method are on three fronts. Firstly, weighting factors associated with vertical and torsional motion in the objective function are determined more reasonably using an iterative procedure rather than preassigned. Secondly, flutter derivatives are identified using a hybrid heuristic and classical optimization method, which integrates a modified artificial bee colony algorithm with the Powell’s algorithm. Thirdly, a statistical bootstrap technique is used to quantify the uncertainties of flutter derivatives. The advantages of the proposed method with respect to other methods are faster and more accurate achievement of the global optimum, and refined uncertainty quantification in the identified flutter derivatives. The effectiveness and reliability of the proposed method are validated through noisy data of a numerically simulated thin plate and experimental data of a bridge deck sectional model.

Aerodynamic flutter instability could lead to the catastrophic collapse of flexible long-span bridges and needs to be prevented. This study investigated the variability of eight experimentally measured flutter derivatives (FDs) for a commonly used a Pasco–Kennewick (PK) section girder using a free vibration technique in a wind tunnel, which provided some new insights into the identification of FDs and supplemented the reliability analysis for buffeting and flutter performance. The aerodynamic uncertainties in terms of the dispersion of flutter coefficients were studied and two implications behind the extraction of FDs were discussed. The statistical and probabilistic behaviors of FDs at different reduced wind speeds were examined before generating sufficient independent random samples using the Monte Carlo (MC) approach. The intercorrelations between experimental FDs quantified by correlation coefficients were also examined and were employed to randomly sample the correlated FDs. The probabilistic flutter solutions in terms of critical wind speed propagated from the FDs uncertainties were studied utilizing step-by-step analysis, which resulted in several multimodal probability distributions of flutter onset. In addition, the role played by each FD on the variation of critical wind speed was discussed. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Flutter derivatives identified from transient (free-decay) vibrations might not be suitable for the analysis of bridge flutter. The application of transient flutter derivatives in the flutter analysis relies on two assumptions: (1) transient flutter derivatives and steady-state flutter derivatives are equivalent and (2) aeroelastic effects are superposable. Both assumptions are challenged in this article. It is shown through transient vibration tests that (1) the aeroelastic-coupling between heaving and rotational motions may switch from one pattern to another as the wind speed varies and (2) some of the transient flutter derivatives may be time-varying. The former implies that the predicted flutter type based on transient flutter derivatives may not be unconditionally consistent with the experimentally observed flutter type; the latter implies the transient flutter derivatives may be physically different from the steady-state flutter derivatives. These two issues undermine the basic assumptions of the flutter analysis of bridges. A possible corollary to this study is that if free vibration is used to predict bridge flutter, we should resort to the steady-state (flutter state) vibration instead of the transient vibration of the sectional model. A revision to the aeroelastic force model is proposed to facilitate the discussion. [ABSTRACT FROM AUTHOR]

Highlights • Critical wind speed for dry-cable galloping of smooth cables based on yaw angle. • Empirical formulae to estimate aero-drag and Strouhal number of yawed cables. • Empirical form of buffeting admittance/indicial derivative functions of cables. • Extraction of aerodynamic-damping/stiffness via flutter derivatives of cables. • Predicting required damping to prevent dry-cable galloping of smooth cables. Abstract Cables of suspension, cable-stayed and tied-arch bridges, suspended roofs, and power transmission lines are prone to moderate to large-amplitude vibrations in wind because of their low inherent damping. Structural or fatigue failure of a cable, due to these vibrations, pose a significant threat to the safety and serviceability of these structures. Over the past few decades, many studies have investigated the mechanisms that cause different types of flow-induced vibrations in cables such as rain-wind induced vibration (RWIV), vortex-induced vibration (VIV), iced cable galloping, wake galloping, and dry-cable galloping that have resulted in an improved understanding of the cause of these vibrations. In this study, the parameters governing the turbulence-induced (buffeting) and motion-induced wind loads (self-excited) for inclined and yawed dry cables have been identified. These parameters facilitate the prediction of their response in turbulent wind and estimate the incipient condition for onset of dry-cable galloping. Wind tunnel experiments were performed to measure the parameters governing the aerodynamic and aeroelastic forces on a yawed dry cable. This study mainly focuses on the prediction of critical reduced velocity (R V cr ) as a function of equivalent yaw angle (β*) and Scruton number (Sc) through measurement of aerodynamic-damping and stiffness. Wind tunnel tests using a section model of a smooth cable were performed under uniform and smooth/gusty flow conditions in the AABL Wind and Gust Tunnel located at Iowa State University. Static model tests for equivalent yaw angles of 0–45° indicate that the mean drag coefficient (C D) and Strouhal number (S t) of a yawed cable decreases with the yaw angle, while the mean lift coefficient (C L) remains zero in the subcritical Reynolds number (Re) regime. Dynamic one degree-of-freedom model tests in across-wind and along-wind directions resulted in the identification of buffeting indicial derivative functions and flutter derivatives of a yawed cable for a range of equivalent yaw angles. Empirical equations for mean drag coefficient, Strouhal number, buffeting indicial derivative functions and critical reduced velocity for dry-cable galloping are proposed for yawed cables. The results indicate a critical equivalent yaw angle of 45° for dry-cable galloping. A simplified design procedure is introduced to estimate the minimum damping required to arrest dry-cable galloping from occurring below the design wind speed of the cable structure. Furthermore, the results from this study can be applied to predict the wind load and response of a dry cable at a specified wind speed for a given yaw angle. [ABSTRACT FROM AUTHOR]

This paper discusses the results of computational fluid dynamics simulations carried out for rectangular cylinders with various side ratios of interest for many civil engineering structures. A bridge deck of common cross-section geometry was also considered. Unsteady Reynolds-averaged Navier–Stokes (URANS) equations were solved in conjunction with either an eddy viscosity or a linearized explicit algebraic Reynolds stress model. The analysis showed that for the case studies considered, the 2D URANS approach was able to give reasonable results if coupled with an advanced turbulence model and a suitable computational mesh. The simulations even reproduced, at least qualitatively, complex phenomena observed in the wind tunnel, such as Reynolds number effects for a sharp-edged geometry. The study focused both on stationary and harmonically oscillating bodies. For the latter, self-excited forces and flutter derivatives were calculated and compared to experimental data. In the particular case of a benchmark rectangular 5:1 cylinder, 3D detached eddy simulations were also carried out, highlighting the improvement in the accuracy of the results with respect to both 2D and 3D URANS calculations. All of the computations were performed with the Tau code, a non-commercial unstructured solver developed by the German Aerospace Center.

The design of long-span bridges is constrained by the uncertainty in the evaluation of flutter velocity. Among all the elements that take part in the flutter assessment, the uncertainty level in experimentally obtained flutter derivatives has the most impact. It is therefore important in the evaluation of flutter velocity to assess the uncertainty which is associated with the adopted experimental method for flutter derivatives. By using a method of coupled motion only to identify eight flutter derivations simultaneously, it is also essential to consider correlations among the points that define the full set of flutter derivatives since they are not independent from one another. In this research, an experimental campaign was carried out to obtain the statistical information of flutter derivatives and to assemble the correlation matrix. Several cases of reliability analyses were performed to illustrate the importance of considering correlation among random variables as well as the significance of uncertainty level in flutter derivatives on bridge flutter failure. Moreover, a study of Reliability Based Design Optimization (RBDO) was carried out to see the influence of correlations among flutter derivatives on the optimum designs. The RBDO of a suspension bridge was performed under probabilistic flutter constraint using Reliability Index Approach (RIA) method, and this methodology was applied to the Great Belt East Bridge. [ABSTRACT FROM AUTHOR]

With the continuous increase of span lengths, modem 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 Ihe 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. [ABSTRACT FROM AUTHOR]

The present paper suggests a hybrid system identification method to estimate the flutter derivatives from coupled free vibration tests. An optimized covariance-based method is used as the initial guess in the modified unifying least squares method. This combination optimizes the accuracy described by the coefficients of determinations between measured and synthesized signals. Flutter derivatives are identified at high wind speeds, close to and even above the critical flutter wind speed. Results for a sharp-edged rectangular section with a width-to-depth ratio B / D = 10 are presented for two different torsional-to-vertical frequency ratios. In one case the torsional frequency are lower than the vertical, due to a high mass moment of inertia, which makes it possible to estimate the flutter derivatives at very high reduced wind speeds. This reveals that the torsional aerodynamic damping derivative A 2 ∗ reaches a positive maximum followed by a continuous decreasing tendency and eventually negative A 2 ∗ values are identified. This implies that torsional flutter for the B / D = 10 section can be avoided if the structural damping is designed to balance the negative torsional aerodynamic damping expressed by the positive peak value for A 2 ∗ . [ABSTRACT FROM AUTHOR]

To analyze the effects of a central stabilizer on the flutter performance at large angles of attack, this study takes the ideal plate as a section of a bridge deck. The aerodynamic characteristics of stationary cross sections are examined using computational fluid dynamics simulations, and the flutter derivatives are extracted by forced vibration. The critical flutter speed of a target bridge is then calculated, and the aerodynamic mechanism of the central stabilizer is discussed from the work done by aerodynamic forces’ perspective. The results show that use of a central stabilizer with lower heights favors flutter stability at smaller angles of attack by improving the participation level of heaving motion, but the stability of the systematic heaving motion will decrease if the stabilizer is too high, leading to galloping. At larger angles of attack, where the movement of a big vortex causes the occurrence of torsional flutter, the stabilizer can hinder the movement of the vortex if they are on the same side, and the critical flutter speed increases with the increase in stabilizer height. [ABSTRACT FROM AUTHOR]

A numerical simulation technique based on computational fluid dynamics (CFD) for determining the time-varying histories of free vibration displacements, velocities, and aerodynamic forces of bridge decks is presented. The weak coupling method is used to address the problem of fluid-structure-interaction (FSI). The flutter derivatives can be conveniently extracted using the numerically simulated displacements, velocities, and aerodynamic forces, which is similar to the procedure adopted in the forced vibration method. First, the identification accuracy of flutter derivatives is validated by comparison with the theoretical results for an ideal thin plate. Then, the flutter derivatives of two typical bridge deck sections, one streamlined and one bluff, are extracted by the proposed method. The results of the streamlined section show good agreement with other methods. However, for the bluff section, noticeable discrepancies exist between different methods. The mean angle of incidence in the free vibration method is shown to be responsible for these disagreements. The strengths of the newly-proposed approach are compared with those of the numerical and experimental forced vibration and experimental free vibration methods. This convenient and effective approach may serve as a building block for extracting flutter derivatives and better understanding of the aeroelastic responses of long-span flexible bridges. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Vibration Engineering is the property of Nanjing University of Aeronautics & Astronautics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

An aerodynamic optimization measure of the flutter stability of long-span suspension bridges with truss girder is presented in this paper. At first, the improvement of several kinds of central stabilizers and horizontal stabilizers on flutter stability is examined through series of section model and full aeroelastic model wind tunnel tests. Subsequently, the flutter derivatives of the truss girder with and without stabilizer are identified based on two degrees of freedom coupling free vibration method. Furthermore, based on the identified flutter derivatives, the critical flutter velocities of the truss girder section with and without stabilizer are analyzed through two dimensional flutter analysis method and the critical flutter velocities of the full bridge with and without stabilizer are analyzed through three dimensional method. Afterwards, the influence of each flutter derivative on the flutter stability of the truss girder is investigated. The results indicate that central upper stabilizer can effectively increase the critical flutter velocity of the truss girder. In contrast, the central lower stabilizer and horizontal stabilizer have less influence. Setting up central upper stabilizer leads to an obvious decrease in the value of the flutter derivatives A2* and H2*, while the flutter derivatives H1*, H4*, A1* and A3* are little influenced. The two dimensional and three dimensional flutter analysis results agree well with the sectional model and full model wind tunnel test results respectively. [ABSTRACT FROM AUTHOR]

The flutter instability is one of the most important themes need to be carefully investigated in the design of long-span bridges. This study takes the central-slotted ideal thin flat plate as an object, and examines the characteristics of unsteady surface pressures of stationary and vibrating cross sections based on computational fluid dynamics (CFD) simulations. The flutter derivatives are extracted from the surface pressure distribution and the critical flutter wind speed of a long span suspension bridge is then calculated. The influences of angle of attack and the slot ratio on the flutter performance of central-slotted plate are investigated. The results show that the critical flutter wind speed reduces with increase in angle of attack. At lower angles of attack where the plate shows the characteristics of a streamlined cross-section, the existence of central slot can improve the critical flutter wind speed. On the other hand, at larger angles of attack, where the plate becomes a bluff body, the existence of central slot further reduces the flutter performance. [ABSTRACT FROM AUTHOR]

The minimization method is widely used to predict the dynamic characteristics of a system. Generally, data recorded by experiment (for example displacement) tends to contain noise, and the error in the properties of the system is proportional to the noise level (NL). In addition, the accuracy of the results depends on various factors such as the signal character, filtering method or cut off frequency. In particular, coupled terms in multimode systems show larger differences compared to the true value when measured in an environment with a high NL. The iterative least square (ILS) method was proposed to reduce these errors that occur under a high NL, and has been verified in previous research. However, the ILS method might be sensitive to the signal processing, including the detennination of cutoff frequency. This paper focused on improving the accuracy of the ILS method, and proposed the modified ILS (MILS) method, which differs from the ILS method by the addition of a new calculation process based on correlation coefficients for each degree of freedom. Comparing the results of these systems with those of a numerical simulation revealed that both ILS and the proposed MILS method provided good prediction of the dynamic properties of the system under investigation (in this case, the damping ratio and damped frequency). Moreover, the proposed MILS method provided even better prediction results for the coupling tenns of stiffness and damping coefficient matrix. [ABSTRACT FROM AUTHOR]

Bridges are an important component of transportation. Flutter is a self-excited, large amplitude vibration, which may lead to collapse of bridges. It must be understood and avoided. This paper takes the Jianghai Channel Bridge, which is a significant part of the Hong Kong-Zhuhai-Macao Bridge, as an example to investigate the flutter of the bridge deck. Firstly, aerodynamic force models for flutter of bridges were introduced. Then, wind tunnel tests of the bridge deck during the construction and the operation stages, under different wind attack angles and wind velocities, were carried out using a high frequency base balance (HFBB) system and laser displacement sensors. From the tests, the static aerodynamic forces and flutter derivatives of the bridge deck were observed. Correspondingly, the critical flutter wind speeds of the bridge deck were determined based on the derivatives, and they are compared with the directly measured flutter speeds. Results show that the observed derivatives are reasonable and applicable. Furthermore, the critical wind speeds in the operation stage is smaller than those in the construction stage. Besides, the flutter instabilities of the bridge in the construction and the operation stages are good. This study helps guarantee the design and the construction of the Jianghai Channel Bridge, and advances the understanding of flutter of long afterbody bridge decks. [ABSTRACT FROM AUTHOR]

This paper presents the results of two-dimensional numerical simulations of the flow field around a trapezoidal box-girder bridge section with later cantilevers, experiencing small-amplitude heaving or pitching harmonic oscillations. Unsteady Reynolds-averaged Navier–Stokes equations are solved in conjunction with an eddy-viscosity and an explicit algebraic Reynolds stress model. Flutter derivatives are determined and compared with wind tunnel results, showing fairly good agreement. The degree of sharpness of the deck lower edges is found to play a key role in the aeroelastic behavior of the profile. In particular, the bridge section fully behaves as a bluff body and is prone to low-reduced-wind-speed torsional galloping in the case of perfectly sharp edges. By contrast, the presence of a small radius of curvature in the section lower corners changes the nature of the instability to coupled flutter and significantly postpones the stability threshold, in line with a quasi-streamlined body behavior. Moreover, a wide sensitivity study is carried out, investigating the influence on the self-excited forces of the amplitude of oscillation, mean angle of attack and Reynolds number. In particular, the numerical simulations for the geometry with smooth lower edges highlight the regime transition occurring when the Reynolds number is varied, with significant effects on the flutter derivatives. Finally, the numerical flow visualizations provide a physical explanation of some phenomena observed in the wind tunnel experiments. [ABSTRACT FROM AUTHOR]