Full Bridge Aeroelastic Model Research Articles

Investigation on nonlinear flutter modes competition of a long-span suspension bridge based on full-bridge aeroelastic model tests

Nonlinear flutter has attracted wide attention due to the bottleneck caused by linear flutter theory on flutter-resistant design of super-long-span bridges. The longer the span, the more closely spaced the natural modes, which may cause competition among flutter-modes in a nonlinear flutter, but it is rarely reported so far. To this end, this study experimentally investigates the 3D nonlinear flutter characteristics of a long-span suspension bridge with closely spaced natural modes based on full-bridge aeroelastic model wind tunnel tests. Since there are two unstable flutter-modes within the interested post-critical regime and thus various complex but interesting flutter-modes competition processes were observed, such as continuous modes competition where the vibration amplitude evolution exhibits various different types of “sawtooth” shapes during stable vibration stages. Meanwhile, the complex nonlinear bifurcation behaviors caused by modes competition were also observed. The evolutionary characteristics of flutter-modes competition are analyzed in detail and relevant mechanisms are discussed. As the wind speed increases, the flutter of the studied bridge mainly undergoes a transition from being dominated by the symmetric mode to being dominated by the antisymmetric mode, accompanied by a continuous modes competition zone in between as a transitional zone. The results show that the continuous modes competition will result in a decrease in the maximum amplitude RMS of the full-span, which is beneficial for the structure. But it may also lead to a transient increase in the maximum amplitude of the full-span due to the coupling vibration shape formed by the two significant flutter-modes, which may be bad for the structure.

Buffeting characteristics of cable-stayed box beam bridge based on pressure measurement test of full bridge aeroelastic model

The aim of this study is to explore the buffeting characteristics of cable-stayed box beam bridge based on pressure measurement test of full bridge aeroelastic model. The study includes the influence of turbulence integral length scale and wind yaw angle on the magnitude of buffeting force, spatial distribution of buffeting force, and buffeting displacement response. Under larger turbulence integral length scale, the buffeting force of the box beam and it’s spanwise correlation are larger, which verifies the three-dimensional effect of the buffeting force. It is worth mentioning that, unlike traditional section models, there are differences in the pressure values of the pressure strips in the aeroelastic model at the flow separation point, which may be influenced by the cables. The experimental results of different wind yaw angles show that there is little difference in the buffeting force of the box beam section under the condition of 0°∼15° wind yaw angle, indicating that the maximum buffeting response will occur in the range of 0°∼15° wind yaw angle, which is consistent with the displacement results measured by the aeroelastic model. In addition, by fixing the model with a steel wire, the static and vibration states of the model were achieved. However, due to the high stiffness of the model, it can only generate small buffeting displacement, and the self-excited force component can be almost ignored. There is no significant difference in the results between the static and vibration states.

The Determination of Effective Modes of Wind-Bridge Coupling System Based on Stabilization Clustering Method

Modal identification is the core content of the full-bridge aeroelastic model wind tunnel test. Modal consistency is the most direct and effective basis to ensure that the model and the real bridge meet the similarity criteria. Accurate, simple and fast identification of modal parameters has very important practical significance for the evaluation and correction of aeroelastic models. In this paper, the eigensystem realization algorithm (ERA) and stochastic subspace identification (SSI) is improved, and the automatic identification theory of effective modes of bridge aeroelastic model based on stable clustering method is proposed. The stable diagram eliminates the unstable modes by comparing the results of different system orders, and the pedigree clustering further polarizes the stable modes to obtain multi-order and high-precision system modes. Numerical simulation examples and wind tunnel engineering examples show that the method has high accuracy and good adaptability, and can solve the problem of unstable damping identification results to a certain extent. In the wind tunnel test, the stable clustering method is one of the effective methods to identify the modal of the bridge aeroelastic model excited by the wind environment.

Study on vortex-induced vibration mitigation of parallel bridges by multi-tuned mass damper inerter

This study proposes a novel Multi-Tuned Mass Damper Inerter (MTMDI) system for mitigating the vortex-induced vibration (VIV) responses of parallel bridges. In the proposed system, two individual bridges are linked using two Tuned Mass Damper Inerters (TMDIs). A model of parallel bridges with MTMDI under vortex-induced force is constructed, and two additional schemes wherein each bridge is equipped with a TMDI and a Tuned Mass Damper (TMD) separately are considered. The VIV responses of the parallel bridges are estimated through full bridge aeroelastic model wind tunnel tests. The performance of the MTMDI system with the optimal parameters obtained by the multi-objective optimization technique is compared with the performance of the other aforementioned two schemes. The results indicate that the optimal MTMDI system with smaller attached mass and inertance effectively mitigates the vertical VIV responses when applied to the parallel bridges. The frequency response functions and displacement time histories further demonstrate the effectiveness of the MTMDI system as an attractive alternative to the other schemes. Finally, the sensitivity of performance against variations in each parameter in the MTMDI system is discussed.

Research on improved modal parameter identification method using Hilbert-Huang transform

In the wind tunnel test, the full-bridge aeroelastic model needs to simulate both the shape and dynamic characteristics of the real bridge, and modal parameters are key dynamic parameters. Therefore, it is essential to identify the modal parameters of the model accurately. To get accurate modal parameters of the long-span bridge model in the wind tunnel test, the applications of the Hilbert-Huang transform for modal parameter identification were analyzed in this paper. Then a band-pass filter is designed to filter the original signal so that the intrinsic mode function obtained by empirical mode decomposition can satisfy the single-component signal requirement and eliminate the mode mixing effect effectively. Meanwhile, the endpoint data extension method based on SVM (Support Vector Machine) was presented to restrain the end effects of empirical mode decomposition. Finally, taking the Oujiang Bridge as the engineering background, the improved algorithm was applied to modal parameter identification of the bridge under ambient excitation. The modal parameters such as modal frequency and damping ratio were obtained. The reliability of the improved method was verified by comparing the identified modal parameters with the results of the finite element method, and it turns out that the improved method can reduce the frequency identification error of vertical bend, lateral bend, and torsion to 1.01%, 4.07%, and 1.68%. The results indicated that the improved method based on the Hilbert-Huang transform can accurately identify the main modal parameters of the structure and can be better applied to identify the modal parameters of long-span bridge structures.

Research on Effective Design Methods of Core Beam of Full Bridge Aeroelastic Model

The trial-and-error method is complex and tedious, but often adapted to determine the cross-section sizes of core beams in the design of reduced-scale models. In this study, two optimization methods, the optimization methods in ANSYS and the genetic algorithm, are investigated to optimize the cross-section sizes of core beams of reduced-scale models, which centers around two targeted moments of inertia and a targeted torsion constant. Due to the difficulty of obtaining an analytical solution of the torsion constant, a series of numerical solutions are proposed. Then, taking a U-shaped cross section as an example, the four geometric sizes of the section are optimized by the ANSYS optimization method and the genetic algorithm, respectively. The results of both methods are in good agreement with the targeted values, but the ANSYS optimization method is prone to fall into the local optimization zone and hence could be easily affected by the initial values. The shortcomings of the ANSYS optimization method can be easily avoided by the genetic algorithm, and it is easier to reach the global optimal solution. Finally, taking a suspension bridge with a main span of 920 m as a prototype, the full-bridge aeroelastic model is designed and the genetic algorithm is used to optimize the cross-section sizes of core beams in the bridge tower and the deck. Natural frequencies identified from the aeroelastic model agree well with the target ones, indicating the structural stiffness, which is provided by the core beams, has been modelled successfully.

Modal Parameter Identification of Time-Varying and Weakly Nonlinear Systems Based on an Improved Empirical Envelope Method

The empirical envelope (EE) method based on the amplitude-modulation and frequency-modulation (AMFM) decomposition is effective for identifying the modal parameters of time-varying and weakly nonlinear systems. However, the identification accuracy of the EE method is sensitive to noises which often exist in vibration measurements of real structures. In this study, an improved empirical envelope (IEE) method is proposed to achieve robust modal parameter identification from noisy measurements. Specifically, the idea of sliding window threshold denoising is introduced to reduce the error in the instantaneous envelope induced by abnormal extreme points, and a moving average filter is utilized to reduce the error in the instantaneous frequency induced by high-frequency noises. Two numerical examples and an experimental example of a full-bridge aeroelastic model are analyzed to validate the accuracy of the IEE method and highlight the superiority of the IEE method relative to the original EE method. It is concluded that the IEE method is robust to measurement noises (the considered signal-to-noise ratios include 5–90[Formula: see text]dB) and that the IEE method is more accurate than the EE method. Hence, the IEE method serves as a promising alternative for modal parameter identification of time-varying and weakly nonlinear systems.

Design, fabrication, and dynamic testing of a large-scale outdoor aeroelastic model of a long-span cable-stayed bridge

To overcome the limitations of existing experimental methods (including wind tunnel tests and field measurement experiments) for the study of bridge wind engineering, the research group at the Dalian University of Technology recently proposed to study the wind-resistance behaviours of long-span bridges through large-scale outdoor full-bridge aeroelastic models in natural wind. Several full-bridge aeroelastic models have been constructed, including a 1:50 model of a long-span cable-stayed bridge, which had a total length of 41.76 m and a height of 6.0 m. This paper systematically introduces the design, fabrication, and dynamic testing of the aeroelastic model. Taking the safety, adjustability, durability, and cost of the aeroelastic model into account, new approaches for the design of the main girder envelope, core beam of the bridge tower, and connections of the aeroelastic model are proposed. Free vibration tests and ambient vibration tests were utilised to measure the modal parameters of the aeroelastic model. The identified modal parameters were consistent with those calculated by finite element analysis, suggesting that the design and fabrication of the model were valid. The representative wind field data and measured buffeting responses of the aeroelastic model were presented.

Optimization of long-span suspension bridge erection procedure considering flutter risk in mixed extreme wind events

During the erection stage of the suspension bridge, its critical flutter wind speed is continuously varying due to changing structural dynamic properties including mass and stiffness. On the other hand, the wind climate is also varying greatly seasonally or even monthly during the bridge erection procedure. This work proposes an analytical framework to optimize the deck erection timeline under complex wind climate attacks. Xihoumen Bridge built at Chinese southeastern coast is taken as a calculation example. Full-bridge aeroelastic model wind tunnel test was conducted to examine the critical flutter speed at different erection stages. Extreme wind speed for tropical cyclones and synoptic wind are analyzed by tropical cyclone simulation and meteorological records respectively. Results show that the optimal timeline for Xihoumen Bridge is starting in August if a one-month duration is required for each stage. However, if the worst timeline is selected, the flutter risk will be increased 40 times larger. If the construction timeline is flexible for the construction schedule, this research proves that timeline optimization is a more economical and safe approach than structural approaches like storm ropes.

Experimental Study of Mitigation of Wind-Induced Vibration in Asymmetric Cable-Stayed Bridge Using Sharp Wind Fairings

This paper investigated the aerodynamic response features of an asymmetric cable-stayed bridge. The wind resistance design parameters for judging the response were first determined, afterwards the bridge dynamic characteristics were analyzed for subsequent aerodynamic analysis. The vortex-induced vibrations (VIV) and flutter response at various wind fairing angles were then examined by using a 1:50 sectional model in the wind tunnel test. Finally, a 1:150 full bridge aeroelastic model was employed to explore the aerodynamic stability and characteristics of the whole asymmetric bridge under different wind attack angles in various flow fields. The results show that the sharp wind fairings could reduce the VIV amplitude of the steel box girder cable-stayed bridge to some extent, and the example bridge has examined to have enough flutter stability through sectional and full bridge aeroelastic model wind tunnel tests. Unlike symmetric bridges, the bridge’s maximum displacement of first torsion mode shape is at the closure rather than the mid-span, which is the essential reason to lead this unique vibration feature. The results from the present study could highlight the important effect of structural asymmetry and fairing shape to the wind-induced bridge vibration and hence may facilitate more appropriate wind design of asymmetric cable-stayed bridges.

Research on flutter-mode transition of a triple-tower suspension bridge based on structural nonlinearity

As the typical span of suspension bridge increases and multi-tower suspension bridges are developed, the linear flutter theory cannot meet the design requirements of modern flexible bridges, and the study of nonlinear flutter of bridges becomes necessary. The author discovered the flutter-mode transition phenomenon in a full-bridge aeroelastic model wind tunnel test of the Maanshan Bridge; that is, the bridge vibration was transformed from first-order anti-symmetric torsion mode (A-T-1) to first-order symmetric torsion mode (S-T-1) and diverged when the flutter critical wind speed was approached. A vertical bending mode acted as a medium for energy transfer between A-T-1 and S-T-1. This phenomenon greatly increased the critical wind speed of flutter, and therefore it is interesting to study its mechanism. Starting from the nonlinear nature of the bridge structure itself, this paper discusses the mechanism of the flutter-mode transition phenomenon, and analyzes the typical characteristics of flutter-mode transition of Maanshan Bridge in depth. A nonlinear discrete mathematical model of the Maanshan Bridge is built, and the transition between the vertical bending mode and torsional mode of the bridge is realized. Adopting the Mathieu function theory and based on the single-degree-of-freedom vibration equation of the Maanshan Bridge corresponding to each mode, the evolution between A-T-1 and S-T-1 is realized, the mechanism of which is also explained.

Experimental research on the aerodynamic responses of a long-span pipeline suspension bridge

The aerodynamic stability performance of a long-span pipeline suspension bridge is studied based on a 1: 25 full-bridge aeroelastic model using wind tunnel tests. The influences of initial angle of attack, pipeline diameter, pipeline number, and turbulence intensity on the aerostatic and buffeting displacements of the girder, and on the wind cable tensile forces are comprehensively investigated. The aerodynamic displacements of the girder along the span were measured by using a video gauge. Analytical expressions are derived to construct the displacements of three-degree-of-freedom motions from the recorded signals, and the differences between the derived formulas and the conventional ones are demonstrated. Recommendations are offered to reduce or even eliminate the potential errors of the convenient habitual formulas. The testing results show that the aerodynamic displacements and wind cable tensile forces of the bridge may depend remarkably on the initial angle of attack, pipeline diameter, pipeline number, and turbulence intensity. Research results of the present work can provide beneficial references for evaluating the wind-resistant performances of bridges of the similar type.

Experimental Study of the Nonlinear Torsional Flutter of a Long-Span Suspension Bridge with a Double-Deck Truss Girder

The purpose of this study is to investigate the nonlinear torsional flutter of a long-span suspension bridge with a double-deck truss girder. First, the characteristics of nonlinear flutter are studied using the section model in the wind tunnel test. Different aerodynamic measures, e.g. upper and lower stabilizers and horizontal flaps, are applied to improve the flutter performance of the double-deck truss girder. Then, the full bridge aeroelastic model is tested in the wind tunnel to further examine the flutter performance of the bridge with the optimal truss girder. Finally, three-dimensional (3D) flutter analysis is performed to study the static wind-induced effects on the nonlinear flutter of the long-span suspension bridge. The results show that single-degree-of-freedom torsional limit cycle oscillations occur at large amplitudes for the double-deck truss section at the attack angles of [Formula: see text] and [Formula: see text]. The upper and lower stabilizers installed on the upper and lower decks, respectively, and the flaps installed near the bottoms of the sidewalks can all effectively alleviate the torsional flutter responses. Meanwhile, it is found that the torsional flutter responses of the truss girder in the aeroelastic model test are much smaller than those in the section model test. The 3D flutter analysis demonstrates that the large discrepancies between the flutter responses of the two model experiments can be attributed to the additional attack angle caused by the static wind-induced displacements. This finding highlights the importance and necessity of considering the static wind-induced effects in the flutter design of long-span suspension bridges.

Wind-induced vibrations and suppression measures of the Hong Kong-Zhuhai-Macao Bridge

A series of wind tunnel tests, including 1:50 sectional model tests, 1:50 free-standing bridge tower tests and 1:70 full-bridge aeroelastic model tests were carried out to systematically investigate the aerodynamic performance of the Hong Kong-Zhuhai-Macao Bridge (HZMB). The test result indicates that there are three wind-resistant safety issues the HZMB encounters, including unacceptable low flutter critical wind speed, vertical vortex-induced vibration (VIV) of the main girder and galloping of the bridge tower in across-wind direction. Wind-induced vibration of HZMB can be effectively suppressed by the application of aerodynamic and mechanical measures. Acceptable flutter critical wind speed is achieved by optimizing the main girder form (before: large cantilever steel box girder, after: streamlined steel box girder) and cable type (before: central cable, after: double cable); The installations of wind fairing, guide plates and increasing structural damping are proved to be useful in suppressing the VIV of the HZMB; The galloping can be effectively suppressed by optimizing the interior angle on the windward side of the bridge tower. The present works provide scientific basis and guidance for wind resistance design of the HZMB.

Recent advances, future application and challenges in nonlinear flutter theory of long span bridges

Polynomial-type mathematical models were presented to describe the nonlinear self-excited forces of nonlinear single degree of freedom (SDOF) torsional flutter of bluff bridge decks and nonlinear coupled flutter of streamline-like flat closed box bridge decks. A full bridge analysis method for nonlinear SDOF torsional flutter of long span bridges with bluff decks was then proposed based on the aeroelastic strip theory, and verified via wind tunnel test of full bridge aeroelastic model. A full bridge analysis method of nonlinear coupled flutter of long span bridges was also established based on the aeroelastic strip theory and an approximate linear complex-modal decomposition (ALCMD), and was applied then to the nonlinear coupled flutter analysis of a 688m main-span cable-stayed bridge. The analysis results show that behaviors of self-limiting and single-frequency oscillation of the nonlinear coupled flutter can be exhibited by using the proposed coupled flutter analysis approach. A new concept of performance-based graded evaluation and fortification criteria against flutter of long span bridges was then put forward for further discussions, which will possibly be an important and prosperous field of future applications of the nonlinear flutter theory. To this end, some challenging issues was discussed for further developing nonlinear flutter theory.

A new method for studying wind engineering of bridges: Large-scale aeroelastic model test in natural wind

To overcome the limitations of the existing experimental methods (i.e., wind tunnel test and in-situ measurement) for wind engineering research of bridges, a new experimental method is proposed, i.e., studying the wind-resistant performance of bridges based on large-scale deck sectional models and full bridge aeroelastic models in natural wind. The representative wind field data are offered to briefly verify the feasibility of this experimental method. The Outdoor Experimental Bases for Bridge Wind Engineering of Dalian University of Technology as well as three full bridge aeroelastic models and a large-size steel tower (for deck sectional model and cable aeroelastic model tests) are introduced, and the extensive possible research items are listed. The available sensors and instruments are outlined, which enable many kinds of measurements. The advantages and disadvantages of the newly proposed experimental method relative to the existing ones are commented for deepen the understanding.

Effect of the low-frequency turbulence on the aeroelastic response of a long-span bridge in wind tunnel

The influence of the low frequency turbulence components on the buffeting response of long span bridges was studied through experimental tests performed on a full bridge aeroelastic model in the wind tunnel of the Politecnico di Milano, using an active turbulence generator producing a correlated deterministic harmonic turbulence. The experimental evidence underlined the nonlinear effect of the low frequency incoming turbulence on the dynamic resonant response of the structure at higher frequencies.Numerical simulations are used to explain the bridge behavior considering the variation of the aeroelastic properties of the bridge with the instantaneous angle of attack and reduced velocity. Even though wind tunnel experiment uses an oversimplified wind spectrum with an intentionally high correlation along the main span, it helps to understand the nonlinear interaction between the low frequency and the high frequency buffeting response on a full bridge.

Real-Time Aerodynamics Hybrid Simulation: A Novel Wind-Tunnel Model for Flexible Bridges

Despite rapid development in computational fluid dynamics, semiempirical analyses based on parameters identified from spring-mounted sectional models are still widely used to examine wind-induced effects on bridges. In addition, wind tunnel results from full-bridge aeroelastic models, viewed as the most comprehensive representations, are typically a final check for wind design of long-span cable-supported bridges. There are several well-known limitations associated with conventional wind tunnel testing of both sectional and full-bridge models. For example, structural nonlinearities and large deformations are difficult to simulate in sectional models, and only a limited number of modes can be accurately simulated in full-bridge aeroelastic models. To advance aeroelastic modeling of flexible bridges in the wind tunnel, a slightly different version of the real-time hybrid simulation (RTHS) techniques, frequently used in various branches of engineering, is developed here. Specifically, the skeleton of the sectional or full-bridge model, characterizing the dynamic properties (e.g., mass, damping, and stiffness of the structure), is numerically simulated using computational structural dynamics, while its skin, characterizing the aerodynamic and aeroelastic properties, is physically modeled in the wind tunnel. Aerodynamic inputs (gusts) are applied directly on the skin in the wind tunnel, while aeroelastic inputs (motions) are represented by the simulation outputs of the bridge skeleton. On the other hand, the dynamic inputs to the bridge skeleton are acquired from the measured forces (and moments) on the bridge skin. The interactions between the skeleton and skin of the bridge are accomplished through a system consisting of sensors, a network of electromagnetic actuators, and controllers. The time history of the wind-induced bridge responses can be obtained at the end of the proposed real-time aerodynamics hybrid simulation (RTAHS). The feasibility of the RTAHS methodology is demonstrated by a numerical example involving both linear and nonlinear wind-induced forces on the bridge deck.

Wind-induced nonlinear behaviors of twin-box girder bridges with various aerodynamic shapes

Wind-induced nonlinear oscillations of twin-box girder bridges are very sensitive to the aerodynamic shape of the deck (i.e., slot width ratio (SWR) and wind fairing shape) due to the complicated flow characteristics around the bridge deck. This paper presents a fully integrated finite element (FE) model in time domain, involving a nonlinear aerodynamic force model and a bridge FE model, to allow the investigation of nonlinear oscillation behaviors of long-span twin-box girder bridges with various SWRs and wind fairing shapes. The parameters in integrated FE model were firstly identified by using CFD simulation, and then, the proposed model was validated by conducting wind tunnel testing using sectional models and full-bridge aeroelastic models. It demonstrates that the developed integrated model has the capability of simulating the nonlinear flutter behaviors of twin-box girder bridges with various aerodynamic shapes. Furthermore, the prediction results show that the wind fairing shape has significant impact on the degree of freedom participation in coupled oscillation and failure modes, as well as flutter performance of the bridges. In addition, there is an increase in amplitudes of the limit cycle oscillations with the increase in the SWR of the twin-box girder bridges, and the relationships between the bending-torsional coupled oscillation, failure modes, and SWR of the bridges with anti-symmetric wind fairings are opposite to those with symmetric wind fairings.

Identification and application of six-component aerodynamic admittance functions of a closed-box bridge deck

A colligated residue least square method of auto and cross spectra (CRLSMACS) is presented for identifying six-component aerodynamic admittance functions (AAFs) base on common force and pressure measurement tests in the passive grid-generated turbulent flow. The incomplete spanwise correlation of the buffeting force on the sectional model in the turbulent flow is corrected. The six-component AAFs of a flat closed-box deck of a single-tower cable-stayed bridge are identified with the presented method for the service states without/with wind barriers and the construction state under 0° wind attack angle, respectively. The buffeting responses of the bridge are then calculated for both the service and typical construction sates by using a finite element approach based on the quasi-steady buffeting theory with the tested six-component AAFs to consider the unsteady effect of buffeting forces. The calculated buffeting responses are finally compared with and found to agree well with those obtained via full bridge aeroelastic model tests, verifying the feasibility of the proposed CRLSMACS as well as the reliability of the identified six-component AAFs and the calculated buffeting responses.