Section Model Tests Research Articles

Application of a new empirical model of nonlinear self-excited force to torsional vortex-induced vibration and nonlinear flutter of bluff bridge sections

Long-span bridges are susceptible to vortex-induced vibration (VIV) and flutter in different reduced wind range. Currently, VIV and flutter are considered as two different types of wind-induced vibration and different empirical models were proposed. The possibility of building a universal empirical model for both torsional VIV and nonlinear flutter was explored. In the previous study, a new empirical model was proposed for describing aerodynamic nonlinearities during soft flutter of a bluff bridge section with a medium side ratio. In this study, the empirical model was refined and extended to both torsional VIV and nonlinear flutter for a general bluff body, especially for a flat bridge deck, which is more common in long-span bridges. In the empirical model, aerodynamic nonlinear damping effect was modeled by a cubic velocity term and its applicability was validated by a series of elastically-mounted sectional model tests of a flat twin-side-girder bridge deck. The results indicated that the proposed empirical model was suitable for predicting the stable amplitude of torsional VIV and nonlinear flutter, although the motion-induced “pure force” varies with side ratios. It was found that torsional VIV and soft flutter share the same nonlinear damping mechanism during the development of LCO.

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.

A novel two-degree-of-freedom model of nonlinear self-excited force for coupled flutter instability of bridge decks

This paper aims to propose a novel model for predicting the nonlinear heave-torsion coupled flutter instability of flat bridge decks. The nonlinear oscillatory system during coupled post-flutter instabilities was modeled as a weak perturbation of the classical linear flutter theory. A novel nonlinear self-excited force model was then proposed by introducing extra nonlinear terms in classical linear model to consider the effects of nonlinear aerodynamic damping, amplitude-dependent vibration mode and the coupling of aerostatic deformation. An efficient algorithm for parameters identification and solving of the nonlinear coupled oscillator was also developed. The effectiveness of the proposed analytical framework was validated through an elastically-supported sectional model test in estimating the self-sustained vibrations during post-critical states of a typical closed-box bridge deck.

A novel long short-term memory neural-network-based self-excited force model of limit cycle oscillations of nonlinear flutter for various aerodynamic configurations

Due to the strong nonlinear properties of the entire flutter process [including growth stages, decay stages and steady limit cycle oscillations (LCOs)], the generalization of the self-excited force model for the entire flutter process of bluff bodies is a very critical issue. This paper proposes a self-excited force model based on a novel long short-term memory (LSTM) neural network to simulate the entire flutter process for various leading-edge configurations. To obtain the dataset, the nonlinear flutter with the growth stages, decay stages and steady LCOs for different leading-edge aerodynamic configurations is investigated by a series of two-degrees-of-freedom spring-suspended sectional model tests. Based on the measured flutter responses and self-excited forces in the tests, a data-driven self-excited force model is proposed on the basis of a novel LSTM neural network. Considering that the nonlinear dynamic system is very sensitive to the accuracy of the model parameters, the Newmark-$$\beta $$ method is incorporated into the LSTM networks and forms a closed-loop process to restrain the error amplification effects and improve the model robustness, that is, the response calculated from the output of LSTM (the self-excited force) by the Newmark-$$\beta $$ method is set as the input of LSTM at the next step rather than the measured response. To validate the performance of the proposed model, the flutter critical wind speed, time history of oscillation and self-excited forces, steady-state oscillation amplitude and flutter development process predicted by the model are compared with the test results. The comparison indicates that the predicted results agree well with the test results, meaning that the proposed model has high accuracy, generalization and robustness in describing the nonlinear characteristics of the flutter for various aerodynamic configurations.

Experimental Investigation on the Nonlinear Coupled Flutter Motion of a Typical Flat Closed-Box Bridge Deck.

The nonlinear post-flutter instabilities were experimentally investigated through two-degree-of-freedom sectional model tests on a typical flat closed-box bridge deck (width-to-depth ratio 9.14). Laser displacement sensors and piezoelectric force balances were used in the synchronous measurement of dynamic displacement and aerodynamic force. Beyond linear flutter boundary, the sectional model exhibited heave-torsion coupled limit cycle oscillation (LCOs) with an unrestricted increase of stable amplitudes with reduced velocity. The post-critical LCOs vibrated in a complex mode with amplitude-dependent mode modulus and phase angle. Obvious heaving static deformation was found to be coupled with the large-amplitude post-critical LCOs, for which classical quasi-steady theory was not applicable. The aerodynamic torsional moment and lift during post-critical LCOs were measured through a novel wind-tunnel technique by 4 piezoelectric force balances. The measured force signals were found to contain significantly higher-order components. The energy evolution mechanism during post-critical LCOs was revealed via the hysteresis loops of the measured force signals.

Modelling nonlinear aerodynamic damping during transverse aerodynamic instabilities for slender rectangular prisms with typical side ratios

The transverse aerodynamic instabilities of rectangular cylinders with three typical side ratios (width-to-depth-ratio as 2:1, 1:1 and 1:2) were investigated through a series of elastically-supported sectional model tests. Experimental results indicate that side ratio plays an important role in the phenomena of transverse instabilities and a larger side ratio B/D generally corresponds to a stronger interaction of VIV and galloping. For side ratio B/D ​= ​2, all test cases exhibited unsteady galloping starting from the Kármán vortex resonance wind speed. When Scruton number is larger than a threshold value between 12.1–19.4, the unsteady galloping of B/D ​= ​1 shows a separate behavior of VIV and galloping with a twofold-amplitude phenomenon. Whereas, side ratio B/D ​= ​0.5 exhibited a pure transverse VIV. The feasibility of classical quasi-steady theory was found not able to predict the onset wind speeds and stable amplitudes. An empirical model was established to consider the aerodynamic nonlinearity by two amplitude-dependent damping terms and aerodynamic unsteadiness by expressing aerodynamic parameters as functions of reduced frequency. The empirical model was validated, having a satisfactory accuracy in predicting the vibration amplitudes of unsteady galloping and VIV. The proposed model represents a promising tool in engineering applications where the interference of VIV and galloping is concerned.

Characterization of vibration amplitude of nonlinear bridge flutter from section model test to full bridge estimation

This paper presents a comprehensive study of nonlinear flutter characteristics of a bridge deck section through free vibration wind tunnel testing and theoretical analysis. The section model is spring-supported in a single degree of freedom (SDOF) in torsion and 2DOFs in both vertical direction and torsion, respectively. The amplitude-dependent aerodynamic damping and other response characteristics are determined through use of Hilbert Transform of response time histories at different wind speed of smooth flow. An approach is proposed to extract flutter derivatives as nonlinear functions of amplitude of torsional motion at various reduced wind speeds. The flutter derivatives are then used to estimate the nonlinear flutter response of bridge section and a prototype suspension bridge with a main span length of 1700 ​m. The results showed that the magnitude of negative aerodynamic damping increases with increasing wind speed but decreases with vibration amplitude. The flutter of this bridge example is initialed from torsion but the coupled vertical motion further generates negative damping, thus reduces the flutter onset wind speed and increase the vibration amplitude. The estimation using three-dimensional bridge model with coupled vertical and torsional modal responses leads to increase in flutter onset wind speed and decrease in flutter amplitude as compared to section model estimation.

Vibration control of vortex-induced vibrations of a bridge deck by a single-side pounding tuned mass damper

This paper proposes a new method to mitigate vortex-induced vibrations (VIVs) of a bridge deck using a single-side pounding tuned mass damper (SS-PTMD). The SS-PTMD is a passive control device and comprises an undamped tuned mass with a pounding boundary covered with viscoelastic (VE) materials layer. A nonlinear force model for describing impact behavior of VE materials is used to simulate the response of a single degree of freedom (SDOF) system controlled by a SS-PTMD. The free pounding experiments are performed to determine the model parameters of impact force and validate the simulation method. The optimal design of SS-PTMD for SDOF system subjected to sinusoidal excitation is carried out by numerical optimization, and the optimized SS-PTMD is applied to control the vertical VIVs of a bridge deck. The control performance is experimentally examined by elastically mounted section model tests in wind tunnel. In addition, the classical wake oscillator model is used to predict the behavior of the coupled fluid-structure system under VIV and explore the control performance of the SS-PTMD. The experimental results show that the maximum response of the bridge deck model was reduced by 94% when a SS-PTMD with mass ratio of 2% was applied. It is also shown that nonlinearity in vortex shedding forces has little influence on control performance of SS-PTMD optimized under sinusoidal excitation.

Nonlinear post-flutter behavior and self-excited force model of a twin-side-girder bridge deck

The nonlinear aeroelastic behavior of a typical bluff bridge section, i.e., open twin-side-girder bridge deck, was investigated through a series of spring-suspended sectional model (SSSM) tests in the post-flutter state. When the reduced wind speed exceeded linear aeroelastic limits, the sectional model underwent significant limit cycle oscillation (LCO) characterized by a quasi-harmonic torsional vibration with slight heave-torsion coupling effect. The stable amplitudes of post-flutter LCOs increased in a roughly linear way with reduced wind speed. The nonlinear self-excited force (NSEF) was measured by a novel force measurement technique and validated by comparing the calculated post-flutter responses with experiments. The measured NSEF contained significant 2nd and 3rd order nonlinear harmonic components. Based on the measured NSEF signals and equivalent energy principle, a NSEF model suitable for large amplitude of vibration was proposed and then verified by comparing its predicted response with experimental results. The identified aerodynamic parameters further indicated that the mechanism of post-flutter LCOs was due to the negative aerodynamic damping provided by the linear term as an energy source to drive the growth of vibration amplitude and the nonlinear positive aerodynamic damping provided by the 3rd order angular velocity term as a stabilizing factor of self-limitation phenomenon.

Vortex-induced vibration of a 5:1 rectangular cylinder: A comparison of wind tunnel sectional model tests and computational simulations

Considered to be representative of a generic bridge deck geometry and characterised by a highly unsteady flow field, the 5:1 rectangular cylinder has been the main case study in a number of studies including the “Benchmark on the Aerodynamics of a Rectangular 5:1 Cylinder” (BARC). There are still a number of limitations in the knowledge of (i) the mechanism of the vortex-induced vibration (VIV) and (ii) of the turbulence-induced effect for this particular geometry. Extended computational and wind tunnel studies were therefore conducted by the authors to address these issues. This paper primarily describes wind tunnel and computational studies using a sectional model in an attempt to bring more insight into Point (i). By analysing the distribution and correlation of the surface pressure around an elastically mounted 5:1 rectangular cylinders in smooth and turbulent flow, it revealed that the VIV was triggered by the motion-induced leading-edge vortex; a strongly correlated flow feature close to the trailing edge was then responsible for an increase in the structural response.

Effect of stabilizer on flutter stability of truss girder suspension bridges

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.

Experimental investigation of correction factor for VIV amplitude of flexible bridges from an aeroelastic model and its 1:1 section model

Evaluation of the maximum amplitudes of vortex-induced vibrations (VIV) in suspension bridges is mainly relied upon section model wind tunnel tests of bridge decks. Extrapolation to prototype responses requires addition correction to take into account the differences both in structural mode shape and in spanwise correlation of excitation forces between the section model and the prototype. The paper presents the results of VIV amplitudes measured on an aeroelastic model and on its section model with the same size of cross-section. The aeroelastic model is a new, elastically multi-supported one which is capable of reproducing the closely-spaced vertical modes of a suspension bridge. The vortex-induced vibrations for a number of vertical modes were successfully measured from the aeroelastic model test in smooth flow. The spring-mounted section model having the same size of cross-section as the aeroelastic model was also tested in smooth flow at the same mass, damping ratio and vibration frequency. It is shown that both the VIV onset wind velocity and lock-in range for each mode of vibration are in good agreement between the aeroelastic model and the section model. The aeroelastic model consistently produces a roughly 30% higher maximum amplitude than the section model for the observed modes of vibration. It is confirmed that the combined three-dimensional (3D) effects due to mode shape and imperfect correlation of excitation forces amplify the VIV amplitudes and disregarding these effects may underestimate the VIV amplitudes for section model tests. A correction factor of 1.3 for the VIV amplitude of vertical modes in suspension bridges may be adopted for practical use when extrapolating the section-model results to their corresponding full-scale values.

Nonlinear mathematical model of unsteady galloping force on a rectangular 2:1 cylinder

This paper aims at establishing a reliable mathematical model for unsteady galloping instability or the combined effects of VIV and galloping. Instead of only basing on galloping displacement, the unsteady galloping force (UGF) is measured directly from spring-suspended sectional model tests through an improved force measurement technique. The measured UGF is found to be able to numerically reconstitute the galloping displacement responses with acceptable accuracy. In establishing an UGF model from the measured force, an energy equivalent principle (EEP) is proposed to simplify the modeling procedure and identifying aerodynamic parameters. The obtained UGF force model contains a third-order and fifth-order velocity terms to consider aerodynamic damping nonlinearities, and the unsteady effect of galloping is modeled by considering the variation of aerodynamic parameters with reduced wind speed. It is found that the negative aerodynamic damping provided by the first-order and third-order velocity terms is the source of the power driving the development of the unsteady galloping, while the positive aerodynamic damping provided by the fifth-order velocity term acts as a stabilizer making the galloping amplitude stable finally. The effectiveness of proposed UGF model and EEP in parameters identification was validated by comparing the numerically calculated galloping amplitude with experimental results.

Improving the aerodynamic performance of Vila-Real Bridge deck-section

The susceptibility of bridge decks to vortex induced oscillations can be addressed through wind-tunnel testing. This paper considers the case of the Vila-Real Bridge, in the north of Portugal, which has the highest deck above ground (230m), among concrete-deck bridges cable-stayed in the central plane. It has a single-cell rectangular box girder with a wide top flange supported by regularly spaced inclined struts. Aeroelastic studies of this precise type of deck seem nonexistent in the literature.Results of sectional model tests are presented for a selection of three distinct angles of attack and three deck configurations, including a solution, alternative to the usual mitigation measures, that solved the susceptibility to vortex induced vibration of the deck and that has no relevant additional design or building costs.With the proposed approach, bridge designers may be able to relegate the use of sections with high aerodynamic performance – but that can be more costly, pose a greater challenge in the construction, or require more time to completion – and the use of mitigation measures, to cases in which they prove to be absolutely necessary.

Aeroelastic stability of two long-span arch structures: A collaborative experience in two wind tunnel facilities

In this paper, a rare example of comparison between sectional and full-aeroelastic model tests is presented. Interestingly, the experiments were conducted in two very different wind tunnel facilities by different research teams. The study concerns two long-span steel arch structures recently built in Milan, Italy, for Expo 2015 World Fair. The structures have only aesthetic purposes and are therefore very flexible and light, which makes them sensitive to wind-induced excitation and prone to aeroelastic instabilities. In particular, in smooth flow an interesting phenomenon of interference between vortex-induced vibration and galloping was observed up to high values of the Scruton number. This aeroelastic instability is very dangerous as large-amplitude vibrations can occur in wind speed ranges where they are not expected, at least for what classical theories for vortex-induced vibration and quasi-steady galloping are concerned. Moreover, the provisions of Eurocode 1 resulted clearly unsuitable and non-conservative to address such a phenomenon. Despite the differences in the facilities and in the models, a good agreement was found between the results obtained in the two laboratories. The major discrepancies were observed in the transitional behavior for intermediate values of the Scruton number, the sectional model showing a more unstable behavior. The tests on the full-aeroelastic model also allowed considering the effect of the angle of wind exposure of the structures, both the in-plane and the out-of-plane vibrations of the arches and the dynamic response to turbulent wind. In particular, a set of tests in smooth flow was performed accounting for the presence of the other arch and of the surrounding buildings. A particular dynamic excitation of the in-plane flexural modes of the structures was observed in well defined ranges of flow speeds when one arch is in the wake of the other. Finally, both experimental campaigns highlighted the need for the installation of tuned mass dampers on the real structures to guarantee their safety. The effectiveness of these devices against the observed galloping-type instability was also verified through wind tunnel tests on the full-aeroelastic model.

Ensayos de viento para el Puente de la Constitución de 1812 sobre la Bahía de Cádiz

The 1812 Constitution Bridge over the Cádiz Bay has been subjected to several wind studies and tests using the most advanced methodology and techniques that the current state of the art allows. Full aeroelasticity tests in a boundary layer tunnel have been carried out, taking into account the whole configuration of the bridge during the in-service state, and also considering the most critical stage during the construction. No risk of aerodynamic instability has been found for the design wind speed. Furthermore, static section model tests for determination of static load coefficients for drag, lift and moment, and dynamic section model tests for simulation of the vertical and torsional vibrations of the bridge induced by vortex shedding and buffeting were also carried out. An exhaustive tests program was also developed to investigate the wind action on reference vehicles, evaluating the good performance of the windshield.

Evaluation on bridge dynamic properties and VIV performance based on wind tunnel test and field measurement

Full scale measurement on the structural dynamic characteristics and Vortex-induced Vibrations (VIV) of a long-span suspension bridge with a central span of 1650 m were conducted. Different Finite Element (FE) modeling principles for the separated twin-box girder were compared and evaluated with the field vibration test results, and the double-spine model was determined to be the best simulation model, but certain modification still needs to be made which will affect the basic modeling parameters and the dynamic response prediction values of corresponding wind tunnel tests. Based on the FE modal analysis results, small-scaled and large-scaled sectional model tests were both carried out to investigate the VIV responses, and probable Reynolds Number effects or scale effect on VIV responses were presented. Based on the observed VIV modes in the field measurement, the VIV results obtained from sectional model tests were converted into those of the three-dimensional (3D) full-scale bridge and subsequently compared with field measurement results. It is indicated that the large-scaled sectional model test can probably provide a reasonable and effective prediction on VIV response.

Investigation on the effect of vibration frequency on vortex-induced vibrations by section model tests

Higher-mode vertical vortex-induced vibrations (VIV) have been observed on several steel box-girder suspension bridges where different vertical modes are selectively excited in turn with wind velocity in accordance with the Strouhal law. Understanding the relationship of VIV amplitudes for different modes of vibration is very important for wind-resistant design of long-span box-girder suspension bridges. In this study, the basic rectangular cross-section with side ratio of B/D=6 is used to investigate the effect of different modes on VIV amplitudes by section model tests. The section model is flexibly mounted in wind tunnel with a variety of spring constants for simulating different modes of vibration and the non-dimensional vertical amplitudes are determined as a function of reduced velocity U/fD. Two 'lock-in' ranges are observed at the same onset reduced velocities of approximately 4.8 and 9.4 for all cases. The second 'lock-in' range, which is induced by the conventional vortex shedding, consistently gives larger responses than the first one and the Sc-normalized maximum non-dimensional responses are almost the same for different spring constants. The first 'lock-in' range where the vibration frequency is approximately two times the vortex shedding frequency is probably a result of super-harmonic resonance or the "frequency demultiplication". The main conclusion drawn from the section model study, central to the higher-mode VIV of suspension bridges, is that the VIV amplitude for different modes is the same provided that the Sc number for these modes is identical.

Wind tunnel test on aerodynamic effect of wind barriers on train-bridge system

To investigate the aerodynamic effect of wind barriers on a high-speed train-bridge system, a sectional model test was conducted in a closed-circuit-type wind tunnel. Several different cases, including with and without barriers, with different barrier heights and porosity rates, and with different train arrangements on the bridge were taken into consideration; in addition, the aerodynamic coefficients of the train-bridge system were measured. It is found that the side force and rolling moment coefficients of the vehicle are efficiently reduced by a single-side wind barrier, but for the bridge deck these values are increased. The height and porosity rate of the barrier are two important factors that influence the windbreak effect. Train arrangement on the bridge will considerably influence the aerodynamic properties of the train-bridge system. The side force and rolling moment coefficients of the vehicle at the windward side are larger than at the leeward side.

Vortex-induced oscillations of bridges: theoretical linkages between sectional model tests and full bridge responses

Vortex-induced oscillation is a type of aeroelastic phenomenon, to which extended structures such as long-span bridges are most susceptible. The vortex-induced vibration (VIV) behaviors of a concerned bridge were investigated conventionally in virtue of wind tunnel tests on string-mounted sectional models. This necessitates the building of a linkage between the response of the sectional model and that of the prototype structure. Although many released literatures have related to this issue and provided suggestions, there is a lack of consistency among them. In this study, some theoretical models describing the vortex-induced structural motion, including the linear empirical model, the nonlinear empirical model and the modified (or generalized) nonlinear empirical model, are firstly reviewed. Then, the concept of equivalent mass density is introduced based on the principle that an equal input of energy should result in identical structural amplitudes. Based on these, the theoretical linkages between the amplitude of a section model and that corresponding to the prototype bridge are discussed with different analytical models. Theoretical derivation indicates that such connections are dependent mainly on two factors, one is the presupposed shape of deformation, and the other is the theoretical VIV model employed. The theoretical analysis in this study shows that, in comparison to the nonlinear empirical models, the linear one can result in obvious larger estimations of the full bridges\' responses, especially in cases of cable-stayed bridges.