RESEARCH ON A FLUTTER STABILITY CONTROL MEASURE OF A FABRICATED STEEL TRUSS BRIDGE

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1 RESEARCH ON A FLUTTER STABILITY CONTROL MEASURE OF A FABRICATED STEEL TRUSS BRIDGE He Xiaohui, Wang Qiang, Zhang Chenglong, Zhang Shunfeng and Gao Yaming College of Field Engineering, PLA University of Science & Technology, Nanjing, China hxhjcy@163.com; wangqiangjs@sohu.com; zjuphoenix@gmail.com; @qq.com; gym6609@163.com Received July 2016, Accept March 2017 No. 16-CSME-84, E.I.C ABSTRACT In order to improve the flutter stability of a certain type fabricated steel truss bridge, a method of setting guiding plates is proposed. Based on the two-dimensional 3 DOF coupling flutter method (2d-3DOF method), and by use of the numerical wind tunnel established by computational fluid dynamics (CFD), the flutter stability control measures of setting guiding plates are simulated. Through CFD numerical simulation, the flow field characteristics, flutter derivatives and critical flutter speed of original and guiding-plated models are obtained. It is found that for a certain type fabricated steel truss bridge, the guiding plates can improve its flutter stability. Thus, the feasibility and reliability of setting the guiding plates are proved, and the foundation for its further application in practical projects is laid. Keywords: guiding plates; fabricated steel truss bridge; 2d-3DOF coupling flutter method; flutter stability; control measures. ÉTUDE SUR LES MESURES DE CONTRÔLE DE LA STABILITÉ DE LA VIBRATION D UN PONT EN TREILLIS D ACIER RÉSUMÉ Dans le but d améliorer la stabilité des vibrations d un certain type de pont en treillis d acier, une méthode d installation de plaques de guidage est proposée. En se basant sur la méthode de couplage des vibrations bidimensionnelles à trois degrés de liberté et l utilisation d une soufflerie numérique définie par la méthode des fluides numériques (MFN), les mesures de contrôle de la stabilité des vibrations par l installation de plaques de guidage, sont simulées. Par la simulation numérique, les caractéristiques du champ de vibration, les dérivés de la vibration et la vitesse critique d apparition des vibrations des modèles originaux et des modèles avec plaques de guidage, sont obtenues. Il a été constaté que pour un certain type de pont en treillis d acier, les plaques de guidage peuvent améliorer la stabilité. La faisabilité et la fiabilité des plaques de guidage sont prouvées, et les fondements de l application pratique sont reconnus. Mots-clés : plaques de guidage; pont en treillis d acier; méthode 2D-3DOF stabilité de la vibration; mesures de contrôle. Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2,

2 1. INTRODUCTION The span of fabricated steel truss bridges is increasing significantly because of the improving design and construction levels. Hence, taking measures to improve the flutter stability is becoming more and more important. There are a lot of flutter control measures. With the practicality and reliability taken into consideration, passive aerodynamic control measures are applied more widely than others [1, 2]. A central stabilizer was set up on Japan s Akashi Kaikyo Suspension to improve its stability critical flutter speed [3 6]. In China, a guiding plate was installed on stiffening beams of Runyang Bridge to improve its flutter stability [7]. Yang [8] and Cao [9 11] of Tongji University, also carried out a lot of research in flutter controlling mechanism of central stabilizers and central slots on bridges. On this basis, a flutter control measure in complex cross-section of the assembly steel truss bridge is proposed. Through CFD numerical simulation, the flow field characteristics, flutter derivatives and critical flutter speed of different models are obtained. 2. CFD SIMULATION To investigate a flutter stability control measure for a fabricated steel truss bridge, a typical cross-section is selected. Its flutter stability is simulated with CFD method and CFD-ACE+ software technology platform [12 14] CFDs Equations 1. The continuity equation: 2. Reynolds equations: u x + ν = 0, (1) y u t + u u x + ν u y = 1 p ρ x + µ eff + ( ) u µ eff + ( u µ eff x x y x ν t + u ν x + ν ν y = 1 p ρ y + µ eff + ( ) u µ eff + ( u µ eff x y y y ( 2 u x ) u y 2 ) + F x, (2) ( 2 ν x ) ν y 2 ) + F y, (3) 3. k-ε turbulence model: k t + u k x + ν k ( y = µ + µ )( t 2 k σ k x ) k y 2 + G k + ρε, (4) ε t + u ε x + ν ε ( y = µ + µ )( t 2 ε σ ε x ) ε y 2 + ε k (C 1εC k +C 2ε ρε), (5) where ρ is the fluid density; µ is the dynamic viscosity; µ t is the turbulent viscosity; u,v are the fluid velocities in the x,y direction components; p is the fluid force acting on the unit; F x,f y are forces acting on the fluid micro units. µ eff is the equivalent coefficient of viscosity. σ k is the turbulent stress. ε is the turbulent dissipation rate. G k is the turbulent kinetic energy. C 1,C 2, and C k are the correlation model parameters. The equation of the Reynolds number is Re cr = ν cr D/ν = 2820 > The flow state is turbulent flow, what s more, the turbulent model is the k-ε turbulent model because the hypothesis precondition of this turbulent model is completely turbulent fluid flow, and the k-ε turbulent model is the most widely used in the engineering application. 182 Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2, 2017

3 Fig. 1. Original model. Fig. 2. Guiding-plated model Geometric Model Figure 1 shows a typical section model of the bridge. The main structure is divided into the upper structure, connecting structure and a lower structure [15, 16]. Because the upper structure and lower structure belong to a bluff body, the Guiding Plate I and Guiding Plate II are set up on them. Figure 2 shows a bridge section model with guiding plates. The height of Guiding Plate I is h = 1/2H. The length of Guiding Plate II is l = 1/2L (H,L are the dimensions given in Fig. 2) Meshing In order to ensure the simulation accuracy and computational efficiency, the sub-regional structure mesh is used. The computational domain closer to the bridge sections is meshed with dense grids, while the computational domain far from the bridge sections with sparse grids. Fig. 3 shows the grids. The forced vibration method is adopted. Dynamic meshing technology is used to make the bridge move by sine law [17]. In order to calculate unsteady aerodynamics forces of this sectional model in forced vibration, the forced vibrations in study are all considered to vibrations with small swing and the model is seen as grid model. Through setting different frequencies in forced vibration, the forced vibration in simulation becomes closer to the real conditions. The frequency of pure torsional forced vibration is f = 2 Hz. The amplitude is α 0 = 2 ; initial phase is ϕ = 0 ; drifting displacement is h = 0 m. The frequency of pure vertical bending forced vibration is f = 2 Hz; the amplitude is α = 0 ; the initial phase is ϕ = 0 ; and the drifting displacement is h 0 = 0.01 m. Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2,

4 Fig. 3. Computational domain grids. 3. NUMERICAL RESULTS AND ANALYSIS 3.1. Pure Torsional Motion Simulation Results Analysis Figures 4 and 5 show the response signals of the lift coefficient and the torsion moment coefficient in different models when the test wind velocity is U = 20 m/s. The lift coefficient and the torque coefficient are dimensionless units. The equation for lift coefficient is F V C V = 1/2ρU 2 BL. The equation for the torsion moment coefficient is C M = M 1/2ρU 2 BL, where F V and M is the lift force and torsion moment; ρ is the air density; U is the wind speed; B is the width of bridge sections; D is the height of bridge sections; and L is the length of bridge sections. From Figs. 4 and 5 it can be seen that the adjustment times of the torsion moment coefficient and the lift coefficient response signals in the original model are both about 1.0 second and that in the guiding-plated model are both about 1.2 seconds. Hence, with the guiding plates, the adjustment times of the response signals change little. When the response signals are stable, with the guiding plates, the absolute value of the torsion moment coefficient and the lift coefficient become smaller. It means that, the guiding plates can reduce the aerodynamic coefficients (the torsion moment coefficient and the lift coefficient) and improve the flutter stability. With a steady aerodynamic force and a wind velocity of U = 20 m/s, Figs. 6 to 9 show the pressure distribution of the original model and the guiding-plated model in one pure torsional motion cycle, which correspond to T /4,T /2,3T /4 and T time slots. For convenience, the pressure area is divided into 3 parts: A, B and C. 184 Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2, 2017

5 Fig. 4. Response signals of the lift coefficient in different models. Fig. 5. Response signals of the torsion moment coefficient in different models. Through Figs. 6 to 9, comparing the original model pressure distribution with the guiding-plated model pressure distribution in one pure torsional motion cycle, it can be seen that, for different models, the high and low pressure distribution trends are approximately the same, but their values are significantly different in some areas. 1. The high pressure part of the original model in area A is significantly larger than that of the guidingplated model. 2. The negative pressure part of the original model in area B is significantly larger than that of the guiding-plated model. 3. The negative pressure part of guiding-plated model in area C is significantly larger than that of the original model. Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2,

But on the leeward side, the negative pressure does not change obviously. Under the same conditions, Figs.

6 Fig. 6. Pressure distribution of the original model and the guiding-plated model at T /4 time. In summary, the installation of guiding plates can greatly change some parts of the pressure field, and reduce the difference between the high pressure and negative pressure on the windward side. But on the leeward side, the negative pressure does not change obviously. Under the same conditions, Figs. 10 to 13 show the velocity distribution of the original model and the guiding-plated model in one pure torsional motion cycle, which correspond to T /4,T /2,3T /4 and T time slots. Besides sub-areas A C, the velocity area is further divided into D, E and F. Through Figs. 10 to 13, comparing the velocity distribution between the original model and the guiding-plated model in one pure torsional motion cycle, it can be observed that, for different models, the high and low velocity distribution 186 Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2, 2017

Fig. 7. Pressure distribution of the original model and the guiding-plated model at T /2 time. trends are roughly the same, but their values are significantly different in some areas.

7 Fig. 7. Pressure distribution of the original model and the guiding-plated model at T /2 time. trends are roughly the same, but their values are significantly different in some areas. The velocities of the guiding-plated model in area A, E and F are much larger than those of the original model. It means that, by use of the guiding-plates, the bridge model tends to be more streamlined Pure Vertical Bending Motion Simulation Results Analysis Pure vertical bending motion simulation results are similar to the pure torsional motion simulation results, which are not described here because of limited space. Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2,

8 Fig. 8. Pressure distribution of the original model and the guiding-plated model at 3T /4 time. 4. FLUTTER DERIVATIVES AND FLUTTER CRITICAL WIND SPEED ANALYSIS In the bridge vibration research, flutter derivatives can be considered as a direct response to the value and sign of the work done by aerodynamic [16]. And they represent the vibration divergence essence. Figure 14 shows a comparison of flutter derivatives between the original model and the guiding-plated model. V r is the reduced wind velocity, where U is wind velocity; f is the vibration frequency; B is the model width. The equation is V r = U/ f B. The reduced wind velocity is dimensionless, so we prefer to select the V r rather than U, f, and B. 188 Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2, 2017

9 Fig. 9. Pressure distribution of the original model and the guiding-plated model at T time. From Fig. 14, when the guiding plates are installed, the basic trend of 8 flutter derivatives is not changed, but there are a few differences. Through calculating the flutter derivate, the flutter critical wind speed can be calculated through least squares methods and by the Scanlan s Flutter critical wind speed equation. The derivatives H1 through A 4 represent these flutter derivatives. 1. After the guiding plates are installed, the absolute value of H1 decreases, but it remains negative, and the trend is not changed. So, it means that, aerodynamic damping H1 caused by lifting moment of vertical velocity is reduced. 2. After the guiding plates are installed, H 4 increases at first. When V r = 1.5, starts to decrease. The Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2,

Fig. 10. Velocity distribution of the original model and the guiding-plated model at T /4 time. decreasing start point of is earlier than the original model by half of a reduced wind velocity.

10 Fig. 10. Velocity distribution of the original model and the guiding-plated model at T /4 time. decreasing start point of is earlier than the original model by half of a reduced wind velocity. The decreasing rate of H4 also becomes larger. 3. After the installation of the guiding plates, the absolute value of A 4 is reduced. After V r = 1.75, the decreasing rate of A 4 also decreases. Moreover, the change point of from negative to positive is earlier than the original model by 0.25 reduced wind velocity. For a certain type fabricated steel truss bridge, the first symmetric vertical bending frequency is tested as Hz. It is taken as the bridge vertical bending frequency. The first symmetrical torsional frequency is tested as Hz. And it is taken as the bridge torsional frequency. Through calculation, the original model and guiding-plated model flutter critical wind speeds are shown in Table 1. According to the analysis above, we can get the parameters of bridge sections as given in Table Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2, 2017

Fig. 11. Velocity distribution of the original model and the guiding-plated model at T /2 time. As can be seen from Fig. 15, the intersection of the curve is (V rc,x C ) is (2.9,1.

2π After computation, we can obtain the flutter critical wind speed of the original and guiding-plated models as 16.3 and 22 m/s, respectively.

11 Fig. 11. Velocity distribution of the original model and the guiding-plated model at T /2 time. As can be seen from Fig. 15, the intersection of the curve is (V rc,x C ) is (2.9,1.8), the bridge is in a flutter critical state. And the equation is U C = Bω hx c V rc. 2π After computation, we can obtain the flutter critical wind speed of the original and guiding-plated models as 16.3 and 22 m/s, respectively. From the analysis above, the setting of the guiding plates brings a good effect in improving bridge aerodynamic stability [18]. This method can be implemented in a real bridge as a practical measure. One term of aerodynamic damping caused by lifting moment of vertical velocity is given as follows: ρ 2 B 6 /2m h I Ω hα A 1H 2 cosθ 1 and ρ 2 B 6 /2m h I A 1H 3 cosθ 2. After the installation of guiding plates, the absolute of A 1 is reduced, but still always negative, and the trend is not changed. So the aerodynamic damping caused by lifting moment of vertical velocity is reduced. Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2,

Table 1. Flutter critical wind speeds. Original model (m/s) Guiding-plated model (m/s) 16.3 22 Table 2. Parameters of bridge section. B (m) m (kg/m) I (kg m 2 /m) f h f α ξ h ξ α 4 11212.7 22202.8 0.

12 Table 1. Flutter critical wind speeds. Original model (m/s) Guiding-plated model (m/s) Table 2. Parameters of bridge section. B (m) m (kg/m) I (kg m 2 /m) f h f α ξ h ξ α Fig. 12. Velocity distribution of the original model and the guiding-plated model at 3T /4 time. 192 Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2, 2017

Fig. 13. Velocity distribution of the original model and the guiding-plated model at T time. 5. CONCLUSIONS The following can be concluded by the analysis above: 1.

13 Fig. 13. Velocity distribution of the original model and the guiding-plated model at T time. 5. CONCLUSIONS The following can be concluded by the analysis above: 1. The pressure on the windward side of the bridge can be significantly reduced by the guiding plates. 2. The bridge model tends to be more streamlined with the guiding plates. 3. By incorporating the guiding plates, the flutter derivatives are changed. The flutter critical wind speed can be changed from 16.3 to 22 m/s. The effect of flutter control measures is significant. Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2,

14 Fig. 14. Flutter derivatives comparison between the original and the guiding-plated model. 194 Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2, 2017

15 REFERENCES 1. Yang, Y.X., Zhou, R. and Ge, Y.J., Practical flutter control method for long-span bridges, Journal of Tongji University, Vol. 7, No. 1, pp , Mastsumo, M., Shirato, H., and Shijo, R., Flutter stabilization of long span bridges, in Proceeding of the 2nd international symposium on advances in wind&structures, Toyko, Japan, June 13 15, pp , Sato, H., Kusuhara, S. and Ogi, K. et al., Aerodynamic characteristics of super long-span bridges with slotted box girder, Journal of Wind Engineering and Industrial Aerodynamics, Vol. 88, No. 2, pp , Tanaka, H., Design of super-long-span suspension bridge on aero dynamics, Proceedings of Bridges into 21st Century, Hong Kong: H.K. Institution of Engineering, Vol. 10, No. 5, pp , Zhou, L.R., Yong, X. and James, M.W. et al., Temperature analysis of a long-span suspension bridge based on field monitoring and numerical simulation, Journal of Bridge Engineering, Vol. 21, No. 1, pp , State Key Laboratory for Disaster Reduction in Civil Engineering of Tongji University, Wind-resistant performance investigation for Runyang Bridge, State Key Laboratory for Disaster Reduction in Civil Engineering of Tongji University, Shanghai, China, Yang, Y.X., Ge, Y.J. and Xiang, H.F., Coupling effects of degrees of freedom in flutter instability of long-span bridges, Department of Bridge Engineering, Tongji University, Shanghai, China, pp , Cao, F.C., Influence of central slot on bridge box girder s flutter instability, Journal of Tongji University (Natural Science), Vol. 30, No. 5, pp , Yang, Y.X., Ge, Y.J. and Xiang, H.F., Flutter controlling effect and mechanism of central stabilizer, Journal of Tongji University (Natural Science), Vol. 2, pp , Scanlan, R.H. and Rosenbaum, R., Introduction to the Study of Aircaraft Vibration and Flutter, The MacMillan Company, New York, USA, Kaimal, J.C., Spectral characteristics of surface-layer turbulence, Quarterly Journal of the Royal Meteorological Society, Vol. 98, No. 417, pp , Zhu, Z.W. and Gu, M., A CFD-AM-CSD method on rapid prediction of the flutter spectral characteristics of surface-layer turbulence, Quarterly Journal of the Royal Meteorological Society, Vol. 47, No. 7, pp , Ge, Y.J. and Tanaka, H., Aerodynamic stability of long-span suspension bridges under erection, Journal of Structural Engineering, Vol. 126, No. 12, pp , Xie, L., Zhang, W.M. and Zong, Z.H., Restart iteration method for time-domain flutter analysis of bridge structures based on ANSYS, Journal of Southeast University (Nature Science Edition), Vol. 1, No. 3, pp , Yang, Y.X., Two-dimensional flutter mechanism and its application for long-span bridges, Tongji University, Shanghai, China, Diana, G., Bruni, S. and Collina, A. et al., Aerodynamic challengers in super long span bridge design, in A. Larsen (Ed.), Bridge Aerodynamics, Balkema, Rotterdam, pp , Schewe G. and Larsen A., Reynolds number effects in the flow around a bluff bridge deck across section, Journal of wind Engineering Industrial Aerodynamics, Vols , pp , Xiang, H., Wind Resistance Design Guidebook for High Way Bridges, China Communication Press, Beijing, Transactions of the Canadian Society for Mechanical Engineering, Vol. 41, No. 2,

Flutter instability controls of long-span cable-supported bridge by investigating the optimum of fairing, spoiler and slot

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