Flutter Derivatives Of Bridge Decks Research Articles

Identification of linear and nonlinear flutter derivatives of bridge decks by unscented Kalman filter approach from free vibration or stochastic buffeting response

This study presents an unscented Kalman filter (UKF) approach for identification of linear or nonlinear flutter derivatives (FDs) of bridge decks from free vibration or buffeting response time history. The nonlinear FDs, which are dependent on torsional vibration amplitude, are represented in polynomial functions of torsional displacement. The augmented state variables of the two degrees of freedom (2DOF) bridge deck system, which include bridge deck motions and unknown FDs, are estimated simultaneously with the UKF approach based on response measurement data. Firstly, the steady-state vortex-induced vibration and flutter of a streamlined bridge deck section are used to illustrate the performance of UKF approach in extracting nonlinear FDs. The equivalent linear FDs are also identified from the same response data which reveals the deficiency of the linear model. Secondly, the stochastic buffeting responses of the bridge deck contributed from two modal responses with linear FDs are generated, and the performance of UKF approach with unknown excitations is examined. It is pointed out that the buffeting response must be separated into two modal response components, such that the unknown buffeting force excitations can be modeled as white noise processes, and the UKF approach offers satisfactory identification of FDs.

Free vibration numerical simulation technique for extracting flutter derivatives of bridge decks

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.

Effects of fundamental factors on coupled vibration of wind-rail vehicle-bridge system for long-span cable-stayed bridge

In a wind-vehicle-bridge (WVB) system, there are various interactions among wind, vehicle and bridge. The mechanism for coupling vibration of wind-vehicle-bridge systems is explored to demonstrate the effects of fundamental factors, such as mean wind, fluctuating wind, buffeting, rail irregularities, light rail vehicle vibration and bridge stiffness. A long cable-stayed bridge which carries light rail traffic is regarded as a numerical example. Firstly, a finite element model is built for the long cable-stayed bridge. The deck can generally be idealized as three-dimensional spine beam while cables are modeled as truss elements. Vehicles are modeled as mass-spring-damper systems. Rail irregularities and wind fluctuation are simulated in time domain by spectrum representation method. Then, aerodynamic loads on vehicle and bridge deck are measured by section model wind tunnel tests. Eight vertical and torsional flutter derivatives of bridge deck are identified by weighting ensemble least-square method. Finally, dynamic responses of the WVB system are analyzed in a series of cases. The results show that the accelerations of the vehicle are excited by the fluctuating wind and the track irregularity to a great extent. The transverse forces of wheel axles mainly depend on the track irregularity. The displacements of the bridge are predominantly determined by the mean wind and restricted by its stiffness. And the accelerations of the bridge are enlarged after adding the fluctuating wind.

Insight into coupled forced vibration method to identify bridge flutter derivatives

The flutter derivatives of bridge decks can be efficiently identified using the experimentally and/or numerically coupled forced vibration method. This paper addresses the issue of inherent requirement for adopting different frequencies of three modes in this method. The aerostatic force components and the inertia of force and moment are mathematically proved to exert no influence on identification results if the signal length (t) is integer (n=1,2,3...) times of the least common multiple (T) of three modal periods. It is one important contribution to flutter derivatives identification theory and engineering practice in this study. Therefore, it is unnecessary to worry about the determination accuracy of aerostatic force and inertia of force and moment. The influences of signal length, amplitude, and frequency ratio on flutter derivative are thoroughly investigated using a bridge example. If the signal length t is too short, the extraction results may be completely wrong, and particular attention should be paid to this issue. The signal length t=nT (<TEX>$n{\geq}5$</TEX>) is strongly recommended for improving parameter identification accuracy. The proposed viewpoints and conclusions are of great significance for better understanding the essences of flutter derivative identification through coupled forced vibration method.

Effects of Exponentially Modified Sinusoidal Oscillation and Amplitude on Bridge Deck Flutter Derivatives

With the use of a computational fluid dynamics (CFD) numerical simulation, in this study an unusual exponentially modified sinusoidal (EMS) oscillation was forcibly imposed on deck section to simulate amplitude-varying self-excited forces. This approach facilitated the investigation of the influence of EMS transient oscillation and amplitude on self-excited forces and flutter derivatives. Study results show that for an ideal thin plate, the sensitivities of H2*, H4*, A2*, and A4* to oscillation decaying/diverging ratio (ξ) were higher than those of H1*, H3*, A1*, and A3*. With different amplitudes, ξ, and reduced wind velocities, the self-excited forces of one flat plate and two bluff bridge decks were numerically calculated and the flutter derivatives were extracted and compared with the theoretical and experimental results. If |ξ| < 0.1, its influence was almost negligible, by which the traditional sinusoidal oscillation technique was validated. The heaving and torsional amplitudes had different influences on each flutter derivative. The influences were also related to deck cross sections and reduced wind velocities. The proposed numerical simulation of EMS oscillation enables a better understanding of the influence of oscillation amplitude and ξ on bridge deck flutter derivatives.

Bridge deck flutter derivatives: Efficient numerical evaluation exploiting their interdependence

Increasing the efficiency in the process to numerically compute the flutter derivatives of bridge deck sections is desirable to advance the application of CFD based aerodynamic design in industrial projects. In this article, a 2D unsteady Reynolds-averaged Navier-Stokes (URANS) approach adopting Menter׳s SST k-ω turbulence model is employed for computing the flutter derivatives and the static aerodynamic characteristics of two well known examples: a rectangular cylinder showing a completely reattached flow and the generic G1 section representative of streamlined deck sections. The analytical relationships between flutter derivatives reported in the literature are applied with the purpose of halving the number of required numerical simulations for computing the flutter derivatives. The solver of choice has been the open source code OpenFOAM. It has been found that the proposed methodology offers results which agree well with the experimental data and the accuracy of the estimated flutter derivatives is similar to the results reported in the literature where the complete set of numerical simulations has been performed for both heave and pitch degrees of freedom.

On the identification of flutter derivatives of bridge decks via RANS turbulence models: Benchmarking on rectangular prisms

In this paper, the ability of two RANS-based turbulence models, the standard k–ω and the k–ω sst (shear-stress-transport formulation), in predicting flutter derivatives of elongated rectangular prisms with different aspect ratios is investigated. Strengths and limitations of the employed methodology are highlighted via comparisons with available experimental results, aiming at identifying some operative indications for choosing a suitable modeling approach (not much time-consuming and suitably accurate), useful for engineers facing the aerodynamic design of bridge structures. The influence of discrepancies among experimental measurements and RANS-based numerical results on the aeroelastic stability of bridge-like structures is also discussed.

Some new insights into the identification of bridge deck flutter derivatives

In the identification of flutter derivatives using coupled free vibration technique, the influences of implied approximations are assessed in this study. For a thin flat plate section and three representative deck sections of long-span bridges, KH1∗, KH2∗, KA1∗, KA2∗, K2H3∗, K2H4∗, K2A3∗, and K2A4∗ are demonstrated to be dependent on reduced wind velocity, especially at lower reduced wind velocities. This is contrary to the commonly used assumption of these parameters being constants. Kh is conventionally used to quantify H1∗, H4∗, A1∗, A4∗, and Kα for H2∗, A2∗, H3∗, A3∗. This means the direct components of aeroelastic motions (h1,α2) are comparatively predominant than the incentive cross components (h2,α1). However, this approximation is only valid for weak modal coupling cases at lower wind velocities. Novel perspectives are provided regarding the subtle underlying complexities in extracting flutter derivatives using coupled free vibration technique. The accuracy in identifying flutter derivatives can be effectively improved by setting close frequencies of coupled modes. The mechanical damping ratio, mass, and mass moment of inertia can be artificially increased to postpone the occurrence of flutter and extend the reduced wind velocity region to acquire sufficient flutter derivatives for flutter analysis. This study may serve as a building block for improving the understanding of flutter derivative identification from coupled free vibration responses, and practical strategies are proposed to improve the identification accuracy.

Identification of flutter derivatives of bridge decks using CFD-based discrete-time aerodynamic models

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.

Direct Approach to Extracting 18 Flutter Derivatives of Bridge Decks and Vulnerability Analysis on Identification Accuracy

The extraction of 18 flutter derivatives of bridge decks from three degree-of-freedom (3-DOF) free vibration data using a novel direct approach is addressed in this study. Different with many conventional methods that construct a system state matrix, this approach directly extracts 18 flutter derivatives using the aeroelastically modified modal parameters. No state matrix is concerned, and thus it is more straightforward from the physical essence viewpoint. The validity and accuracy are demonstrated by a 3-DOF numerical example for bridge deck model. Afterward, the 18 flutter derivatives of two exact bridge decks with representative streamlined and bluff sections are extracted. Detailed deterministic and stochastic vulnerability analyses on identification accuracy of modal parameters and flutter derivatives were conducted for the numerical model and two bridge decks. For the free vibration method, the potential uncertainties in aeroelastic parameter determination are investigated, and the causes of low accuracy of some flutter derivatives (e.g., H4*, A4*, P1∼4*) are attributed to the imperfection of the linear mathematical model, testing technique, and constraint conditions, and inherent low participation and/or coupling intensities of aeroelastic components. The aeroelastic characteristics and the influence of complex aerodynamic coupling on flutter performance of both streamlined and bluff bridge decks are examined and compared to unveil the mechanisms of two kinds of flutter.

On the evaluation of bridge deck flutter derivatives using RANS turbulence models

This paper concerns the capabilities and the limitations of computational fluid dynamic simulations in evaluating the dynamic aeroelastic coefficients currently used to study the bridge deck instability due to wind loading. The attention is focused on the Reynolds-averaged Navier-Stokes (RANS) approach coupled with the k−ω turbulence model, identified as the best compromise between accuracy and computational cost. Firstly, the capabilities of the turbulence model to evaluate the aerodynamic forces acting on static bluff bodies are assessed. Then, the static and dynamic aerodynamic coefficients of the Great Belt East Bridge cross-section are evaluated, and the performances of three widely used turbulence models are compared. Aiming at providing a well-defined modus operandi useful for structural engineers who approach computational flutter derivatives estimation, much attention is devoted to detail the setting of the numerical analyses as well as the interpretation of the results and the comparison to wind tunnel data.

Analytical and experimental study on aerodynamic control of flutter and buffeting of bridge deck by using mechanically driven flaps

A passive control using flaps will be an alternative solution for flutter stability and buffeting response of a long suspension bridge. This method not only enables a lightweight economic stiffening girder without an additional stiffness for aerodynamic stability but also avoid the problems from the malfunctions of control systems and energy supply system of an active control by winglets and flaps. A time domain approach for predicting the coupled flutter and buffeting response of bridge deck with flaps is investigated. First, the flutter derivatives of bridge deck and flaps are found by experiment. Next, the derivation of time domain model of self-excited forces and control forces of sectional model is reported by using the rational function approximation. Finally, the effectiveness of passive flap control is investigated by the numerical simulation. The results show that the passive control by using flaps can increase the flutter speed and decrease the buffeting response. The experiment results are matched with numerical ones.

Extraction of bridge aeroelastic parameters by one reference-based stochastic subspace technique

Without output covariance estimation, one reference-based Stochastic Subspace Technique (SST) for extracting modal parameters and flutter derivatives of bridge deck is developed and programmed. Compared with the covariance-driven SST and the oscillation signals incurred by oncoming or signature turbulence that adopted by previous investigators, the newly-presented identification scheme is less time-consuming in computation and a more desired accuracy should be contributed to high-quality free oscillated signals excited by specific initial displacement. The reliability and identification precision of this technique are confirmed by a numerical example. For the 3-DOF sectional models of Sutong Bridge deck (streamlined) and Suramadu Bridge deck (bluff) in wind tunnel tests, with different wind velocities, the lateral bending, vertical bending, torsional frequencies and damping ratios as well as 18 flutter derivatives are extracted by using SST. The flutter derivatives of two kinds of typical decks are compared with the pseudo-steady theoretical values, and the performance of <TEX>$H_1{^*}$</TEX>, <TEX>$H_3{^*}$</TEX>, <TEX>$A_1{^*}$</TEX>, <TEX>$A_3{^*}$</TEX> is very stable and well-matched with each other, respectively. The lateral direct flutter derivatives <TEX>$P_5{^*}$</TEX>, <TEX>$P_6{^*}$</TEX> are comparatively more accurate than other relevant lateral components. Experimental procedure seems to be more critical than identification technique for refining the estimation precision.

Determination of 18 Flutter Derivatives of Bridge Decks by an Improved Stochastic Search Algorithm

This paper addresses the determination of the 18 flutter derivatives of bridge decks from three degrees-of-freedom (3DOF) free vibration data using an improved stochastic search algorithm (ISSA) combined with the unified least-squares (ULS) method. The ISSA is capable of circumventing the local optimum dilemma in pursuing the optimal solution experienced in the traditional ULS method. The validity and accuracy of the ISSA are demonstrated by one numerical example and two long-span, cable-stayed, bridge deck sections. The attractive merit of using different lengths of vertical, torsional, and lateral vibration data in flutter derivatives identification is investigated. The identification error and modal participations in flutter are easily examined through a decomposition of modal components from the original vibration data. The underlying complexities in aeroelastic parameter identification are studied, and the causes of low accuracy of some flutter derivatives are unveiled. Based on the comparative investigation on the aerodynamic characteristics of typical streamlined and bluff bridge decks, an improved understanding of the coupled bridge flutter is achieved.

Analysis of Flutter Stability of the Xihoumen Bridge in the Completed Stage

Aerodynamic stability is an issue in the wind-resistant design of long-span bridges, flutter is an aerodynamic instability phenomenon that occurs due to interactions between wind and structural motion. The Xihoumen Bridge is the second long suspension bridge in the world, the aeroelastic performance of the Xihoumen Bridge is investigated by wind tunnel testing and an analytical approach. In the case, wind-tunnel testing was performed using an aeroelastic full model of the bridge, and two section models of the bridge. Flutter derivatives of bridge decks are routinely extracted from wind tunnel section model experiments for the assessment of performance against wind loading, the analytical method used here were a two-dimensional flutter analysis and a multi-mode analysis in the frequency domain. The analytical results were compared with the wind tunnel test data; it showed that the flutter analysis results were good agreement with the wind-tunnel test data.

DETERMINATION OF FLUTTER DERIVATIVES OF BRIDGE DECKS BY COVARIANCE-DRIVEN STOCHASTIC SUBSPACE IDENTIFICATION

In this paper, the covariance-driven stochastic subspace identification technique (SSI-COV) was presented to extract the flutter derivatives of bridge decks from the buffeting test results. An advantage of this method is that it considers the buffeting forces and responses as inputs rather than as noises. Numerical simulations and wind tunnel tests of a streamlined thin plate model conducted under smooth flows by the free decay and the buffeting tests were used to validate the applicability of the SSI-COV method. Then, the wind tunnel tests of a two-edge girder blunt type of industrial-ring-road (IRR) bridge deck were conducted under smooth and turbulence flows. The flutter derivatives of the thin plate model identified by the SSI-COV technique agree well with those obtained theoretically. The results obtained for the thin plate and the IRR bridge deck are used to validate the reliability and applicability of the SSI-COV technique to various wind tunnel tests and conditions of wind flows. The results also show that for the blunt-type IRR bridge deck, the turbulence wind will delay the onset of flutter, compared with the smooth wind.

Identification of Flutter Derivatives of Bridge Deck Under Multi-Frequency Vibration

:A multi-frequency vibration method (MFVM) is proposed to identify flutter derivatives of bridge deck. In this method, a bridge deck is forced in vertical or torsional harmonic vibration with linear combination of multi-frequency. Computational Fluid Dynamic (CFD) simulation is conducted using 2D unsteady incompressible Navier-Stokes equations combined with renormalization group (RNG) k  turbulence model, based on improved domain decomposition method. The non-dimensional time histories of lift and moment are fitted by least square method to identify the flutter derivatives of bridge deck. Flutter derivatives of a thin flat plate and the 2nd Nanjing Yangtze River Bridge section are computed. The results are in good agreement with Theodorsen’s theory and wind tunnel test data, which demonstrates the reliability and efficiency of the present approach.

Moving Least Squares (MLS) Method for Identification of Flutter Derivatives of Bridge Decks

Moving Least Squares (MLS) Method for Identification of Flutter Derivatives of Bridge Decks

Identification of flutter derivatives of bridge decks with free vibration technique

The flutter derivatives of bridge decks can be determined in a unique manner on condition that the complex modal parameters of the system at one reduced frequency are obtained. Based on the idea, a new method of identifying the flutter derivatives of bridge decks is proposed and it can overcome some shortcoming of the existing method and extend the applicability of the free vibration technique at high wind velocity. The identified results have agreements with the target ones of an ideal thin-plate section and those of a thin-plate section measured by the forced vibration technique. The proposed method is reliable and effective to extract the flutter derivatives from coupled free vibration.

Data-driven stochastic subspace identification of flutter derivatives of bridge decks

Most of the previous studies on flutter derivatives have used deterministic system identification techniques, in which the buffeting forces and the associated responses are considered as noises. In this paper, one of the most advanced stochastic system identification, the data-driven stochastic subspace identification technique (SSI-DATA) was proposed to extract the flutter derivatives of bridge decks from the buffeting test results. An advantage of the stochastic method is that it considers the buffeting forces and the responses as inputs rather than as noises. Numerical simulations and wind tunnel tests of a streamlined thin plate model conducted under a smooth flow by the free decay and the buffeting tests were used to validate the applicability of the SSI-DATA method. The results were compared with those from the widely used covariance-driven SSI method. Wind tunnel tests of a two-edge girder blunt type of Industrial-Ring-Road Bridge deck (IRR) were then conducted under both smooth and turbulent flows. The identified flutter derivatives of the thin plate model based on the SSI-DATA technique agree well with those obtained theoretically. The results from the thin plate and the IRR Bridge deck helped validate the reliability and applicability of the SSI-DATA technique to various experimental methods and wind flow conditions. The results for the two-edge girder blunt type section show that applying the SSI-DATA yields better results than those of the SSI-COV. The results also indicate that turbulence tends to delay the onset of flutter compared with the smooth flow case.