Bridge Section Model Research Articles

Evaluation of System Identification Methods for Free Vibration Flutter Derivatives of Long-Span Bridges

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.

Buffeting response of a suspension bridge based on the 2D rational function approximation model for self-excited forces

In the last thirty years, the aerodynamic nonlinearities related to the slow variation of the angle of attack produced by large-scale atmospheric turbulence and their impact on the buffeting response of long-span suspension bridges have been a hot topic in wind engineering research. Self-excited forces accounting for such an effect of turbulence have been crucial in predicting the dynamic response of bridge sectional models subjected to multi-harmonic gusts. In contrast, only few studies on full suspension bridges in realistic turbulent flows are available. To fill this gap, the 2D RFA model for self-excited forces, recently developed and experimentally validated by the authors, in this paper is incorporated into a stochastic time-variant state-space framework to assess the nonlinear buffeting response of a suspension bridge. The most important feature of this model is the modulation of the self-excited forces due to the spatio-temporal fluctuation of the angle of attack produced by low-frequency turbulence. Moreover, the nonlinear external buffeting forces are formulated to achieve a reasonable compromise between the conflicting needs of modelling both nonlinear and unsteady effects of wind velocity fluctuations. The model is applied to the Hardanger Bridge in Norway, considering different wind conditions. Indeed, the aerodynamic derivatives of this bridge deck cross-section present a strong dependence on the mean angle of attack. The results emphasise the significant impact on the buffeting response and flutter stability of considering time-variant self-excited forces, though in specific cases the classical time-invariant approach is found to provide accurate predictions of the bridge vibrations. Finally, the paper investigates the sensitivity of the response statistics to the model cut-offs used to separate the low-frequency and the high-frequency turbulence bands.

Experimental investigation on post-flutter characteristics of a typical steel-truss suspension bridge deck

A testing device that was specially developed for large torsional amplitude vibrations was adopted to investigate the nonlinear post-flutter behaviors of a typical steel-truss girder bridge deck. Firstly, a series of free decay vibration tests of a narrow rigid rod model and a section model of the bridge were conducted in still-air to obtain mechanical properties and still-air induced aerodynamic properties. Then, post-flutter experiments of the bridge section model under initial attack angles of −3°, −0°, +3°, +5°, +7°and with different mechanical damping ratios were carried out. Finally, nonlinear and coupling behaviors of the bridge section model during post-flutter were described and analyzed in detail from several different aspects such as aeroelastic center, vibration mode, and wind-induced aerodynamic damping. The results showed that the truss girder section exhibited significant vertical-torsional coupled soft flutter behavior at various attack angles and there was a stable limit cycle oscillation (LCO) and an unstable LCO under a given wind speed near the critical speed. Moreover, the added aerodynamic damping, the coupling vertical deformation, the aerodynamic torsional center, the wind-induced aerodynamic damping, and the soft flutter mode in the post-critical state all exhibited the characteristic of amplitude dependence. Meanwhile, it was found that the coupling vertical deformation was strongly related to the torsional amplitude and wind attack angle. Finally, the effects of mechanical damping on the post-flutter performance were discussed and the results showed that some nonlinear dampers whose damping increased with the increasing amplitude can be adopted to improve the critical flutter speed without deteriorating or even enhancing the post-flutter performance.

Numerical Simulation of Wind-Driven Rain on a Long-Span Bridge

Wind-driven rain (WDR) and its interactions with structures is an important research subject in wind engineering. As bridge spans are becoming longer and longer, the effects of WDR on long-span bridges should be well understood. Therefore, this paper presents a comprehensive numerical simulation study of WDR on a full-scale long-span bridge under extreme conditions. A validation study shows that the predictions of WDR on a bridge section model agree with experimental results, validating the applicability of the WDR simulation approach based on the Eulerian multiphase model. Furthermore, a detailed numerical simulation of WDR on a long-span bridge, North Bridge of Xiazhang Cross-sea Bridge is conducted. The simulation results indicate that although the loads induced by raindrops on the bridge surfaces are very small as compared to the wind loads, extreme rain intensity may occur on some windward surfaces of the bridge. The adopted numerical methods and rain loading models are validated to be an effective tool for WDR simulation for bridges and the results presented in this paper provide useful information for the water-erosion proof design of future long-span bridges.

Using ALE-VMS to compute aerodynamic derivatives of bridge sections

Aeroelastic analysis is a major task in the design of long-span bridges, and recent developments in computer power and technology have made Computational Fluid Dynamics (CFD) an important supplement to wind tunnel experiments. In this paper, we employ the Finite Element Method (FEM) with an effective mesh-moving algorithm to simulate the forced-vibration experiments of bridge sectional models. We have augmented the formulation with weakly-enforced essential boundary conditions, and a numerical example illustrates how weak enforcement of the no-slip boundary condition gives a very accurate representation of the aeroelastic forces in the case of relatively coarse boundary layer mesh resolution. To demonstrate the accuracy of the method for industrial applications, the complete aerodynamic derivatives for lateral, vertical and pitching degrees-of-freedom are computed for two bridge deck sectional models and compared with experimental wind-tunnel results. Although some discrepancies are seen in the high range of reduced velocities, the proposed numerical framework generally reproduces the experiments with good accuracy and proves to be a beneficial tool in simulation of bluff body aerodynamics for bridge design.

Flutter suppression of long-span suspension bridge with truss girder

Section model wind tunnel test is currently the main technique to investigate the flutter performance of long-span bridges. Further study about applying the wind tunnel test results to the aerodynamic optimization is still needed. Systematical parameters and test principle of the bridge section model are determined by using three long-span steel truss suspension bridges. The flutter critical wind at different attack angles is obtained through section model flutter test. Under the most unfavorable working condition, tests to investigate the effects that upper central stabilized plate, lower central stabilized plate and horizontal stabilized plate have on the flutter performance of the main beam were conducted. According to the test results, the optimal aerodynamic measure was chosen to meet the requirements of the bridge wind resistance in consideration of safety, economy and aesthetics. At last the credibility of the results is confirmed by full bridge aerodynamic elastic model test. That the flutter reduced wind speed of long-span steel truss suspension bridges stays approximately between 4 to 5 is concluded as a reference for the investigation of the flutter performance of future similar steel truss girder suspension bridges.

Wake control of vortex shedding based on spanwise suction of a bridge section model using Delayed Detached Eddy Simulation

In this paper, the DDES (Delayed Detached Eddy Simulation) is applied to study the spanwise suction control effect on wind-induced effect of a static bridge deck. Isolated suction holes are arranged on the lower surface of the test model in spanwise direction, and based on previous studies of similar bluff body, a proper distance of spanwise suction was chosen to trigger or amplify the most unstable secondary instability (i.e. Mode A) in wake. The simulation results show that the suction arranged close to the wake has the best control effect on reducing the fluctuating aerodynamic forces. Due to the mean-velocity modification by isolated spanwise suction, the virtual aerodynamic shape modification is generated, which could act as spanwise perturbation to suppress spanwise vortexes. The results indicate that the spanwise suction could trigger or amplify the Mode A instability, and hence lead to the dislocation of the spanwsie vortex or even completely suppress the spanwise vortex. In addition, the spanwise suction control can surpress spanwise vortex shedding in a wide Re range.

The influence of vehicles on the flutter stability of a long-span suspension bridge

The presence of traffic on a slender long-span bridge deck will modify the cross-section profile of the bridge, which may influence the flutter derivatives and in turn, the critical flutter wind velocity of the bridge. Studies on the influence of vehicles on the flutter derivatives and the critical flutter wind velocity of bridges are rather rare as compared to the investigations on the coupled buffeting vibration of the wind-vehicle-bridge system. A typical streamlined cross-section for long-span bridges is adopted for both experimental and analytical studies. The scaled bridge section model with vehicle models distributed on the bridge deck considering different traffic flow scenarios has been tested in the wind tunnel. The flutter derivatives of the modified bridge cross section have been identified using forced vibration method and the results suggest that the influence of vehicles on the flutter derivatives of the typical streamlined cross-section cannot be ignored. Based on the identified flutter derivatives, the influence of vehicles on the flutter stability of the bridge is investigated. The results show that the effect of vehicles on the flutter wind velocity is obvious.

Experimental study on aerodynamic derivatives of a bridge cross-section under different traffic flows

The presence of traffic on a bridge deck has an important primary impact on the bridge cross-section׳s aerodynamic configuration, which may affect the static force coefficients and the aerodynamic derivatives that will in turn influence the self-excited forces acting on the bridge. Compared to the investigations of the traffic effect on the static force coefficients, its effect on the aerodynamic derivatives is rather rarely studied. In the present study, the forced vibration device is adopted in the wind tunnel to test a scaled bridge section model with vehicle models distributed on the bridge deck considering three simulated traffic flows. The influence of vehicles of different traffic flows under different wind attack angles on the aerodynamic derivatives of the bridge with the reduced wind velocity are investigated based on the experimental results. The measured results show that the influence of vehicles on the aerodynamic derivatives of the bridge cannot be ignored. The impacts of vehicles under different traffic flows on the aerodynamic derivatives are different for different aerodynamic derivatives. The effect of vehicles on the aerodynamic is different for different wind attack angles and different for different traffic flow conditions at a certain attack angle.

Wind-Induced Performance of Long-Span Bridge with Modified Cross-Section Profiles by Stochastic Traffic

The presence of traffic on a slender long-span bridge (SLB) deck has two types of primary impacts: (1) modification of the bridge cross-section profiles, which may influence the flutter derivatives and in turn, wind-induced aeroelastic loads acting on the bridge; and (2) additional dynamic loads acting on the bridge including dynamic interactions from the vehicles. As compared to the investigations on the impact of traffic as external dynamic loads, those on the impact from the modification of bridge cross-section profiles are rather rare. A scaled bridge section model with vehicle models distributed on the bridge section has been tested in the wind tunnel laboratory. With the FDs obtained from the wind tunnel experiments of various modified bridge cross-section profiles by stochastic traffic, the present study is to numerically evaluate the impact on the wind-induced performance of the long-span bridge, such as the buffeting response and fatigue damage accumulation.

Impact of Stochastic Traffic on Modified Cross-Section Profiles of a Slender Long-Span Bridge: Wind Tunnel Experimental Investigation

For a slender long-span bridge, the global aeroelastic and aerodynamic phenomena, such as flutter stability and buffeting response, induced by wind turbulence significantly affect the safety and lifetime performance of the bridge. To investigate these phenomena, a wind tunnel experimental technique with bridge section models is typically required to identify some critical aerodynamic coefficients, such as flutter derivatives, which are dependent on the specific profile (shape) of a bridge cross section and the functions of reduced frequencies. Obviously, this practice is based on the assumption that the shape of the cross section of a long-span bridge does not vary over time. Such an assumption may not remain valid when the stochastic traffic on the bridge is considered, because of the simple fact that the presence of vehicles changes the profile of the bridge cross section. The current study aims to provide some insights through experimental assessment of traffic impacts on flutter derivatives of the modified bridge cross section because of the presence of traffic. A bridge section model with scaled vehicle models distributed on the bridge deck is tested in the wind tunnel following the simulated stochastic traffic flow. Several scenarios are tested to provide insights on the variations of the flutter derivatives over different sections along the bridge and at different time instants for the same location. In addition, some extreme situations, such as under evacuation or serious congestion, are also studied.

Wind-induced performance of long-span bridge with modified cross-section profiles by stochastic traffic

The presence of traffic on a slender long-span bridge (SLB) deck has two types of primary impacts: (1) modification of the bridge cross-section profiles, which may influence the flutter derivatives and in turn, wind-induced aeroelastic loads acting on the bridge and (2) additional dynamic loads acting on the bridge including dynamic interactions from the vehicles. As compared to the investigations on the impact of traffic as external dynamic loads, those on the impact from the modification of bridge cross-section profiles are rather rare. A scaled bridge section model with vehicle models distributed on the bridge deck has been tested in the wind tunnel laboratory following the simulated stochastic traffic flow. With the flutter derivatives obtained from the wind tunnel experiments of various modified bridge cross-section profiles by traffic, the present study is to numerically evaluate the impact on the wind-induced performance of the long-span bridge, such as the aeroelastic performance, buffeting response and potential fatigue accumulation.

Buffet suppression in long-span suspension bridges

We study the aerodynamic control of long-span suspension bridges and seek to raise the critical flutter wind speeds, while simultaneously suppressing buffeting. The control system design study is based on a simple flexible bridge section model that interacts with a constant-velocity air stream. A streamlined bridge deck is assumed and non-steady thin aerofoil theory is used to describe the interactions between the bridge deck and the air stream. Classical turbulence models, first developed in the aircraft industry, are used to model the buffet forces acting on the deck. While a wide variety of control systems is possible, we focus on a compensation scheme that can be implemented using passive mechanical components such as springs, dampers and a rack and pinion mechanism. A single-loop control system is investigated that controls a trailing-edge flap by sensing movements of the bridge deck; several such mechanisms are contemplated. The first finding is that the critical wind speed for flutter can be greatly increased, with good robustness characteristics, through passive feedback control. It is also possible simultaneously to suppress flutter using the same passive mechanical controller by solving a passive mixed H 2 / H ∞ control problem. The effect of flexible controller mounting arrangements are considered briefly.

Aeroelastic Control of Long-Span Suspension Bridges

The modeling, control, and dynamic stabilization of long-span suspension bridges are considered. By employing leading- and trailing-edge flaps in combination, we show that the critical wind speeds for flutter and torsional divergence can be increased significantly. The relatively less well known aerodynamic properties of leading-edge flaps will be studied in detail prior to their utilization in aeroelastic stability and control system design studies. The optimal approximation of the classical Theodorsen circulation function will be studied as part of the bridge section model building exercise. While a wide variety of control systems is possible, we focus on compensation schemes that can be implemented using passive mechanical components such as springs, dampers, gearboxes, and levers. A single-loop control system that controls the leading- and trailing-edge flaps by sensing the main deck pitch angle is investigated. The key finding is that the critical wind speeds for flutter and torsional divergence of the sectional model of the bridge can be greatly increased, with good robustness characteristics, through passive feedback control. Static winglets are shown to be relatively ineffective.

Decoupling Free Vibration System of Bridge Section Model

In the paper the free vibration system of bridge section model is designed in order to measure the wind-induced effects on the bridge section model in the wind tunnel. In the system the suspension device is constituted with decoupling sliding components and simple spring suspension. Meanwhile, a set of data measurement and acquisition device based on the Labview is provided in the system. The measurement on the wind-induced static force, flutter and vortex-induced vibration of the bridge section model can be conducted at single degree of freedom or multiple degrees of freedom.

New estimation methodology of six complex aerodynamic admittance functions

This paper describes a new method for the estimation of six complex aerodynamic admittance functions. The aerodynamic admittance functions relate buffeting forces to the incoming wind turbulent components, of which the estimation accuracy affects the prediction accuracy of the buffeting response of long-span bridges. There should be two aerodynamic admittance functions corresponding to the longitudinal and vertical turbulent components, respectively, for each gust buffeting force. Therefore, there are six aerodynamic admittance functions in all for the three buffeting forces. Sears function is a complex theoretical expression for the aerodynamic admittance function for a thin airfoil. Similarly, the aerodynamic admittance functions for a bridge deck should also be complex functions. This paper presents a separated frequency-by-frequency method for estimating the six complex aerodynamic admittance functions. A new experimental methodology using an active turbulence generator is developed to measure simultaneously all the six complex aerodynamic admittance functions. Wind tunnel tests of a thin plate model and a streamlined bridge section model are conducted in turbulent flow. The six complex aerodynamic admittance functions, determined by the developed methodology are compared with the Sears functions and Davenport`s formula.

Identification of aerodynamic parameters for eccentric bridge section model

The equations of motion for bridge deck section model elastically suspended in wind tunnel are formulated about mass center of the system using the Lagrangian approach, accommodating both the elasticity and damping eccentricities in the formulation. The Subsection Extended-Order Iterative Least Square (SEO-ILS) algorithm is developed in the state space for direct identification of system matrices from free vibration data of section model obtained from wind tunnel testing. The flutter derivatives can be extracted straightforwardly from the difference in the system matrices identified at zero wind velocity and at a specific wind velocity, respectively. By making use of complex modal decomposition technique, a procedure is employed to correct the system matrix at zero wind velocity considering both eccentricities. The proposed method is applied to identify the flutter derivatives of a thin plate section model and the section model of a suspension bridge. The results show a favorable agreement between the flutter derivatives of a thin plate obtained with the proposed method and those derived from the analytic formulae. The identified direct flutter derivatives of the suspension bridge section model also are in good agreements with those obtained using Scanlan's method. It is shown that the use of the corrected system matrix at zero wind velocity leads to better accuracy in identifying the flutter derivatives especially at high reduced wind velocity than using the original system matrix, and the eccentricity is found to have more influence on the cross flutter derivatives than on the direct flutter derivatives.

Effects of frequency ratio on bridge aerodynamics determined by free-decay sectional model tests

A series of wind tunnel free-decay sectional model dynamic tests were conducted to examine the effects of torsional-to-vertical natural frequency ratio of 2DOF bridge dynamic systems on the aerodynamic and dynamic properties of bridge decks. The natural frequency ratios tested were around 2.2:1 and 1.2:1 respectively, with the fundamental vertical natural frequency of the system held constant for all the tests. Three 2.9 m long twin-deck bridge sectional models, with a zero, 16% (intermediate gap) and 35% (large gap) gap-to-width ratio, respectively, were tested to determine whether the effects of frequency ratio are dependent on bridge deck cross-section shapes. The results of wind tunnel tests suggest that for the model with a zero gap-width, a model to approximate a thin flat plate, the flutter derivatives, and consequently the aerodynamic forces, are relatively independent of the torsional-to-vertical frequency ratio for a relatively large range of reduced wind velocities, while for the models with an intermediate gap-width (around 16%) and a large gap-width (around 35%), some of the flutter derivatives, and therefore the aerodynamic forces, are evidently dependent on the frequency ratio for most of the tested reduced velocities. A comparison of the modal damping ratios also suggests that the torsional damping ratio is much more sensitive to the frequency ratio, especially for the two models with nonzero gap (16% and 35% gap-width). The test results clearly show that the effects of the frequency ratio on the flutter derivatives and the aerodynamic forces were dependent on the aerodynamic cross-section shape of the bridge deck.

Comparisons of bridges flutter derivatives and generalized ones

The causes of the nonlinearity of self-excited aerodynamic force of bridge are interpreted from such two aspects as amplitude and wind velocity. The concept of “generalized flutter derivative” is proposed, and its physical meaning is illustrated. The graphs of the generalized flutter derivatives of plate and Sutong Bridge section model are plotted. The characteristics of all generalized flutter derivatives are compared and analyzed, and their superiorities are verified. The results indicate that the physical meaning of generalized flutter derivatives are more explicit compared to the traditional ones. It is more convenient to understand the nonlinearity properties of self-excited aerodynamic force of bridge according to the generalized flutter derivatives graphs with the wind velocity as the horizontal coordinate.

Finite element simulation of the wind action over bridge sectional models: Application to the Guamá River Bridge (Pará State, Brazil)

The numerical simulation of the wind action over the Guamá River Bridge (Pará State, north of Brazil) is presented in this work. Aerodynamic and aeroelastic analyses performed previously by experimental techniques in a wind tunnel are reproduced now employing a numerical algorithm. The bridge is idealized by sectional models representing cross-sections at the mid-span of some design decks tested in the wind tunnel, where Jersey barriers and safety fences are also included. Two-dimensional viscous turbulent flows are simulated employing the pseudo-compressibility approach, large eddy simulation (LES), an arbitrary Lagrangean–Eulerian (ALE) formulation and an explicit two-step Taylor–Galerkin method. The finite element method (FEM) is used for space discretizations. The fluid–structure interaction is taken into account considering a partitioned coupling scheme where the fluid and structural fields are solved in a sequential way. The dynamical equilibrium equation is solved using the Newmark's Method. The simulation of the wind action over the Great Belt East Bridge is also included in order to demonstrate the applicability of the present formulation.