Flying Sphere image Museo Ideale L. Da Vinci Mechanisms of the vertical vortex induced vibration of the Storebælt bridge

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1 EACWE 5 Florence, Italy 19 th 23 rd July 2009 Flying Sphere image Museo Ideale L. Da Vinci Mechanisms of the vertical vortex induced vibration of the Storebælt bridge J.M. Terrés-Nícoli and G.A. Kopp University of Granada jterres@ugr.es Wind Engineering Division, CEAMA, Avda. del Mediterraneo s/n, Granada, Spain University of Western Ontario gakopp@uwo.ca Boundary Layer Wind Tunnel Laboratory, The University of Western Ontario, London, Ontario, Canada Keywords: vortex induced vibration, long span bridges, Storebælt Bridge. ABSTRACT Considerable research has focused on the vortex induced vibration of the circular and rectangular cylinders. There are, however, fundamental questions that are still not clear. Modern bridges tend to shapes in between classical bluff bodies and airfoils. There is a need for fundamental physical investigations of the triggering mechanisms of the vortex induced response of these shapes. The Storebælt Bridge in Denmark is a notable example of hexagonal shape common in modern suspension bridges for which the availability of extensive numerical and experimental data at model and full scale makes it a remarkable case study. The fluid-structure interactions which trigger the vertical vortex induced vibration of this bridge was investigated by means of section model tests. The study focuses on the simultaneously measured pressure field and response for different increasing and decreasing wind speeds. 1. INTRODUCTION The scientific study of the flow induced vibration of circular cylinders is vast, starting in the late second half of the 19 th century with the work of pioneers such as Raleigh or Strouhal. Nevertheless, there are still a number of fundamentals that are still not clear. Except for creeping flow at low Reynolds numbers (Re), the flow around a stationary cylinder involves boundary layer separation and two corresponding free shear layers. The flow structure results from the interaction of the shear layers in the wake region. At certain Re, the interaction of the two shear layers results in organized, alternating vortex shedding from each side. The synchronized shedding leads to a fluctuating pressure field on the surface of a stationary body. The cylinder will vibrate under this loading if it is flexible (or linked to sprung system of certain stiffness and damping). It has been observed how the resulting Contact person: J.M. Terrés-Nícoli,, CEAMA - Universidad de Granada, Avda. del Mediterraneo s/n, 18006, Granada, Spain. T: x 31155, F: jterres@ugr.es

2 body motion affects the above described flow structure and forcing. Different vortex shedding modes which may involve single (S) or pairs (P) of vortices shed on each side have been associated to different states (2S, 2P, S+P, see (Brika, 1993), (Williamson & Govardhan, 2004), (Zasso et al, 2008)). It is noted here how significant the differences of the flow structure around an oscillating cylinder are compared to the stationary case and result in the development of forces of different nature and magnitude. The flow around a rectangular prism may involve more mechanisms depending on its chord to depth ratio, including trailing edge vortex shedding (TEVS), leading edge vortex shedding (LEVS), impinging leading edge vortex (ILEV) and interactions among them (vortex interaction, VI), (Mills et al., 2002). It has been observed that this vortex formation and structure is sensitive to perturbations across the mean flow, which, acting at a particular frequency, can trigger the instability at the same frequency (Naudascher & Wang, 1993). Such perturbations may originate by the buffeting background response of the body at its natural frequency. The vortices originating from this excitation can be referred to as motion induced vortices (MIV). The existence of MIV together with the gradual development of a different flow structure due to the body motion, such as those observed for the circular cylinder, enhance the different nature and magnitude of the pressure field and resulting force compared to the stationary case. Modern long and midspan bridges often incorporate aerodynamic leading and trailing edges in order to reduce the significant along wind loading and possibly the strength of the vortices shed at TE (see the recent Third Millenium Bridge, (Terrés-Nicoli, King, & Kim, 2007)). The most practical option is to place a triangular fairing while maintaining the depth necessary to provide the needed vertical stiffness (see Figure 1 for c/d=7). This may justify why hexagonal shapes are becoming so common in bridge decks. The addition of the leading and trailing edges will alter the flow structure mechanisms that correspond to the rectangular prism. The effect maybe more significant at the leading edge where the BL flow over the leading edge surfaces may affect the structure and instability of the impinging shear layer. Depending on the chord to depth ratio the separated flow will or will not reattach along the afterbody. The shape of the trailing edge is not expected to affect the flow structure to the same extent if the flow remains separated in the vicinity of B in Figure 1. If it does reattach permanently or intermittently, one can expect the trailing edge shape may have some effect on the vortex formation and strength of vortices. The complex aerodynamics of bridge decks with these shapes are normally evaluated through intensive experimental programs. However, the fluid-structure mechanisms behind the different aeroelastic phenomena are not well known. A B C Figure 1: Rectangular prism with superimposed triangular leading and trailing edges forming an hexagonal shape with reduced drag features common in modern flexible bridges (c/d=7). The Storebælt Bridge is a notable example of such hexagonal shape. Furthermore, the availability of numerical and experimental data at full and model scale is remarkable. It is noted that it may be among the few bridges where the numerical and physical modeling has been performed via such a wide variety of methodologies including: Section model tests at 1:60, 1:70 and 1:80 scale, Full aeroelastic tests and Taut strip tests. D 1.1 Storebælt full scale observations Notwithstanding the above intensive and long term experimental program, the $3.2 billion Storebælt Bridge experienced large amplitude, unacceptable vortex induced vibrations under winds perpendicular to the deck of speeds in the range of 4 to 10 m/s. The amplitudes were higher than the

3 predicted ones. Two reasons might be pointed out: the lower measured structural damping ( =0.45%, as a fraction of the critical) and the lower than expected turbulence intensity levels, I u 2-9%. The deck was ultimately retrofit by adding guide vanes along the main span (at the lower corners E and F in Figure 2) with the subsequent additional cost. D C Trailing edge E LINE #3 Upper flange Bottom flange Figure 2: Pressure measurement distribution of a typical ring. Three identical rings were located at the midspan and one chord and one half of the chord respectively from the midspan. 19 Center of rotation LINE #2 LINE #4 LINE #5 F LINE #1 Leading edge 45 B A 2. METHODOLOGY The self excited nature of VIV lies on the capability of the motion of the body in modifying the flow structure and hence inducing forces of different nature and magnitude. The understanding of the mechanisms involved requires the investigation of the forcing throughout the different phases of the response, which may differ from the stationary case. Consequently some analytical models have been derived by separately modeling a stationary force and a motion induced force (Sarpkaya, 1979), (Vickery & Basu, 1983). A 1:70 scaled section model was designed and built for this purpose. A central channel under the model s top layer housed 11 miniature pressure scanners and all the corresponding tubes and wires. The weight of the scanners inside the model reached a value over 10% the target mass enforced a lighter than normal design. In order to reach the required stiffness, the deck was made of a carbon fiber cardboard sandwich laminated over a foam mould. The pressure field was investigated in detail with the simultaneously measured response through the different phases of the response from the onset up to the maximum amplitude oscillations. The study was performed for both Vertical and Torsional Vortex Induced Vibration (V-VIV and T-VIV, respectively) and Flutter. This paper focuses on the first. The response was studied when the maximum amplitude wind speed was approached, increasing from lower and decreasing from higher wind speeds. Hereinafter the different responses will be simply referred to as response to increasing and decreasing wind speeds. Laboratory Date Model Scale Aspect Ratio Model Natural Bending mode (Hz) fv(hz) Model V ReD ReB Iu (%) Damping ( air) BLWTL : BLWTL : BLWTL : DMI : n/a DMI : Table 1: Different section model test configurations available in the literature Flutter limit (f.s. m/s) The present test configuration, namely BLWTL 3 is compared in Table 1 with the different historical sectional model configurations of the V-VIV performed at different laboratories. This experimental setup was specifically designed for the study of the simultaneous measurement of the

4 pressure field and response during vertical vortex induced vibration. A remarkably stiff sprung system was designed to achieve a high velocity scale that, given the low critical wind speed (V CR + =1.32), would allow for the pressure field measurement. Consequently the rig support frame was stiffened to avoid any undesired contributions from rig flexibility. Similarly, a stiff design of the carbon fiber sandwich of the section model kept the model modes away from the sprung system frequency so that these would not be excited. The fundamental vertical bending mode was monitored and found at a frequency of 42 Hz, significantly above the 9.78Hz of the simulated vertical mode. The first torsional mode was found at 48 Hz and, hence, no contribution is expected from the inherent model modes. The resulting larger velocity scale (1.44), allowed the investigation of the response domain with a higher resolution in the wind tunnel. Figure 3: Observed Vertical Vortex Induced response observed for different damping ratios and wind speed history compared with previous wind tunnel and full scale data. 3. RESULTS AND DISCUSSION The pressure field could be measured at 14 different stages of the response from the onset wind speed (V OR + ) to the critical maximum amplitude oscillations (V CR + ). Figure 3 presents the observed response (rms values of y r ) for different damping values and wind speed history. The present results are in good agreement with previous experiments (DMI 1 and 2, as per Table 1). The vertical vortex induced response is found to have a hysteric behaviour: different response is observed when the maximum amplitude oscillation wind speed (V cr + ), point C, is approached from lower wind speeds compared to when the wind speed is decreased from V - >V cr +. The former correspond to the path marked as ABCDE, compared to EDFBA for the later, in the figure. The modal mass was in every case matched to the scaled value of the prototype. Hence, differences in the Scruton number between the different available data are only due to changes in damping. The strong sensitivity of V-VIV to the inherent damping can be clearly appreciated in the response domain. A reduction in the maximum

5 amplitude oscillations of around 30%, from to 0.05 is observed when the damping was increased from air =0.15 to 0.33%. Different response is observed for different rates of increasing wind speed. In general, higher values of maximum amplitude oscillations are observed for slower rates in increasing or decreasing wind speeds. This was also clearly observed in the T-VIV (Terrés-Nicoli, Kopp, & King, 2003). 3.1 Onset of the oscillations The onset windspeed (V + OR ) was in every case around 0.8 based on the bridge chord (B) and V + ORD =5.64 based on the bridge depth (D). Similarly, maximum amplitude oscillations are observed for V + CR = 1.32 or V + CRD =9.30. The model by (Komatsu, 1980) predicts a reduced windspeed of 8.96 for the rectangular prism based on the sign of the work done by the pressures along the chord. The onset of the oscillations is well predicted by the proposed relationship by (Shirashi & Matsumoto, 1983)0.83(B/D) which yields 5.85 compared to the actual These models are based on a flow structure scheme that involves ILEV and TEV based on the chord to thickness ratio. The study of the different mechanisms involved in the VIV of rectangular prisms is normally based on the chord over thickness parameter (B/D). The additional two edges of a hexagonal shape let argue whether such study shall be based on the 3 different B/D ratios present: 7.05, 6.14, 4.32, for the Storebælt bridge based on AD, BC and DE, respectively. The three would belong to the same group 3.2<B/D<7.6 in which the separated leading edge shear layer periodically separates and reattaches interacting with the vortex formation at the trailing edge. Naudascher (Naudascher & Wang, 1993) proposed a model domain which predicts possible transverse vibration in mode 2 (n=2) due to ILEV for the present B/D ratios of the Storebaelt at V + ORD =1/St ISLI, where St ISLI is the Strouhal number corresponding to the vortex formation due to the instability and roll up of the impinging shear layer of 0.17 (based on B/D=7.05 and =0). The corresponding onset windspeed is V + ORD =5.87, V + OR = 0.83 which matches the experimental observations in Figure 3. Naudascher s Mode 2 corresponds to the coexistence of two ILEVs through one vibration cycle. Modes 1 and 3 for this B/D ratios appear less probable but possible depending on the particular flow conditions Mean (for Cp distribution. example, Vr= I u or.ring surface B roughness) affecting the vortex formation. This is controlled by the parameter in Naudascher formulation. Cp=0.5 Cp=1 positive negative flow Figure 4: Mean pressure field at onset increasing wind speed (V OR + = 0.96). Model is stationary and free to vibrate. The instability of the impinging shear layer at large Re numbers requires a control mechanism. This control can be obtained by means of transverse sound (Parker & Welsh, 1983)or by the actual body motion. Therefore, even leading edge movements at the natural frequency due to background buffeting response can act as the triggering mechanism of the impinging shear layer instability and the corresponding ILEV formation. Such motion induced ILEV (MI-ILEV) may be responsible for the V-VIV of the Storebaelt. Based on the mean pressure field presented in Figure 4, the separation bubble is anticipated to span from a point located between A and B (tap #4) to a point downstream of the railings near tap #16.

6 Remarkably, the span of the separation bubble d, is found close to the bridge depth (D). The separation bubble located on the bottom flange, around point F, presents a comparable scale. To investigate the ISLI phenomena, the spectra of the pressures on the upper flange of the leading edge were examined. It is noted that at the onset wind speed no significant peak is present anywhere within the separation bubble (Figure 5) whereas at peak at frequency of 8.79 Hz is present elsewhere downstream of it (Figure 6). This frequency corresponds to a St=0.16 based on either (D) or the (d) in good agreement with the St ISLI proposed by Naudascher. Figure 5: Typical spectra of the pressure on locations within the separation bubble at the onset of the oscillations. Model is let free to vibrate amplitude is negligible. Figure 6: Typical spectra of the pressure on locations downstream of the separation bubble at reduced windspeed of Special attention is given to the area near the upper flange of the trailing edge (CD, taps 24-27). The spectra at these locations present another peak at the exact natural frequency f V. Additionally, a broader peak is observed at a higher frequency corresponding to a higher St close to A stronger peak corresponding to this higher St is observed in the spectra of hotwire measurements at different wind speeds in the near wake (Figure 7, top left). From left to right in the spectra of the pressure on tap B27, the first peak would be related to the intermittent interaction of the ISL, the second would be motion induced and the third to TEV as it is postulated below. Similar spectral density peaks at these three frequencies are observed too in the lift force coefficient C L in contrast with the only peak at f V present for the maximum amplitude oscillations.

7 It is postulated here that this frequency, which is not present anywhere except for the trailing edge and the wake is related to vortex shedding from the trailing edge (TEV). TEV would be responsible for the initial vibration at the onset windspeed which will control and lead to the instability of the impinging shear layer, roll up, and subsequent vortex formation. A similar behavior is observed at the bottom flange which has its origin at a separation bubble located around point F and which, as will be shown, is out of phase with the upper flange ILEV. This is found consistent with Group 2 mechanisms as proposed for the heaving motion by (Shirashi & Matsumoto, 1983). Limited hotwire measurements B/2 downstream of the TE but further separated 3D/4 above and below the TE present a distinct peak which corresponds to a St=0.15 which matches the estimate St ISL and that is here related to the same leading edge shear layer (Figure 7 top right). At higher wind speeds, as the magnitude of the oscillations builds up, the dominant frequency in the wake is that of the vertical mode (f V ) and its harmonics (Figure 7, bottom). 3.2 Comparison with full-scale observations The full-scale response (Frandsen J. B., 1999), (Frandsen J., 2001) presented in Figure 3 compares well with the different model response. The response observed at reduced wind speeds around 1.8 correspond to broad band energy content and, therefore, is related to background buffeting response rather than VIV. It is noted that the onset and maximum amplitude oscillations wind speeds and magnitudes are well predicted by the physical modeling. Especially significant is the hysteresis behavior observed in the full scale measurements. A full scale observation of VIV corresponding to decreasing wind speed is marked in Figure 4. Importantly, it is found that the present experiments for decreasing wind speeds are in good agreement with this unusual full scale observation. Figure 7: Spectra of wind speed measurements at points located B/2 downstream of the trailing edge, flash with point C (top left) and B/2 downstream of TE further separated 3D/4 above and below the TE, (top right). Same measurements at maximum amplitude oscillations(bottom).

8 Pressures were measured simultaneously at three locations on the upper surface between the central and side crash barriers of the downstream half. The St numbers derived from the spectra range from 0.08 to The latter result is in good agreement with what has been previously related to ILEV. Nevertheless, as has been described, the region where the full scale pressure measurements were conducted is unaffected by the pressure fluctuations related to TEVS which have been related to a higher St number around 0.20 and is held responsible for the onset of the oscillations. The limited pressure spectra in (Frandsen J., 2001) present a motion induced sole peak at the natural modal frequency which is in good agreement with the observed behavior in the present experiments for the corresponding taps Comparison of the pressure field around the oscillating and stationary deck The pressure field at the onset wind speed compares well with the pressure around the fixed deck measured by Larose by means of a taut strip model (Larose, 1992). The comparison of the mean pressure field is presented in Figure 8, where the rms. values are compared as well. The predicted scales of the separation bubbles at leading and trailing edge are in good agreement. The minor observed differences could be partly due to the different spatial resolution, 48 points of the present 1:70 scale section model compared to 32 of the smaller 1:300 taut strip. A distinctive feature observed in both the mean and rms. results is the pressure distribution around the central crash barrier. A characteristic slope, higher suctions and rms are observed in the section model. This could be due to the slope in the roadways (2.5%) and the central barrier that could not be modeled in the taut strip model. The higher fluctuations around this area seem unimportant for the stationary state but may play a role in the ISLI mechanisms during deck motion. Figure 8: Comparison of the mean pressure distribution of steady sprung mounted deck (dotted line and bars) of the present study with the same around the fixed deck (solid line for suctions and black for pressure), (Larose, 1992) The predicted force coefficients at 0 for the fixed deck from the different available experiments are in a range close to 0 of C L =0.08 to 0.1 for smooth flow. Similar results were also obtained by the integration of the pressure field around the 1:300 taut strip model (Larose, 1992). These values are notably lower that the fluctuating coefficients measured at maximum amplitude oscillation of the present study of C L =+0.46 to -0.3 which emphasizes the nature and magnitude of the motion-induced forces. These values are compared to the static coefficients for the angle of attack due to the apparent wind speed considering the deck s motion. Apparent angles of attack of 3.57 and 2.27 are obtained for the maximum and mean deck speeds which correspond to static coefficients of approximately 0.27 and Even though these are better estimates, they are clearly lower than the observed lift coefficients acting on the vibrating deck. This difference stresses the significance of the motion induced mechanism responsible for doubling the values derived from the above mentioned quasi-static approach.

9 Scale I u (%) ReD air St Sectional model (present) 1: (ISLI) 0.21 (TEV) Larose, Taut strip model, : Frandsen, CFD-FVE, Frandsen, Full scale, Morgenthal (flow vis.), Morgenthal & McRobie, CFD-DVM Selvam and Govindaswamy, Xiaoyang Wu and Kopp, G.A. (flow vis.) 1: Vezza and Taylor, CFD-DVM, : 0.16 Table 2: Different Strouhal numbers available in the literature compared to the present study. Figure 9: Evolution of the force coefficients through the buildup phases of the response. It has been proposed that the build-up of the oscillations involves motion induced mechanisms. It is therefore anticipated that the flow structure, pressure magnitudes and force coefficients of the oscillating deck differ from the stationary case. Not surprisingly, different St numbers are reported by different researchers. The full scale St in Table 2, for example, is based on pressure measurements on the upper flange upstream the trailing edge (around tap #22) and, therefore, unable to capture the frequencies present at the onset that have been related to TEV and which are only observed further downstream or in velocity measurements in the wake. The value of 0.15 is in good agreement with the peaks observed in the present study that have been related to ISLI based on the previously mentioned observations from Nakamura, Naudascher, Shirashi and Matsumoto. Furthermore, most of the computational models focus on the flow around the fixed deck and do not include many details that can significantly alter the flow structure (railings, barriers, roughness, etc.). 3.4 Build up The build-up of higher amplitude oscillations is related to the synchronization of the flow structure triggered by the deck motion, which results in an overall phase shift of the lift coefficient. No significant difference other than the increase in the magnitudes of the pressure and force coefficients

10 is observed throughout the build-up phases except for the region on the upper flange right at the leading edge (taps #1-3). It will postulated that (similarly for the T-VIV) the large amplitude fluctuations at this location play a significant role in the instability and strength of the separated flow around the corner B. The phase averaged pressure field was investigated using the vertical displacement as a reference. A clear sinusoidal response is observed for reduced wind speeds above 1.0. For higher wind speeds the frequency component that was associated to TEV was not present in the near wake velocity measurements nor in the spectra of the pressures. The dominant frequency in the flow is equal to f V. It is postulated that a typical Karman street of TEV acts as the control mechanism for the ISLI. Alternate impinging leading edge vortices (ILEV) both on the upper and bottom flanges are responsible for the response. Similarly TEV will be related to the onset of torsional T-VIV oscillations. The lift responsible of maximum amplitude oscillations leads the response in a phase of 90, approximately (within the phase averaging resolution). The synchronization of higher amplitude oscillations is enhanced by a slowly varying phase shift of approximately from 130 at the onset wind speed to 90 at maximum amplitude oscillations (Figure 10). This is consistent with a typical resonant response, where at resonance the force is out of phase and therefore the total work per oscillation cycle is positive (Den Hartog, 1984). In this state, the work done by the force is dissipated in damping. That explains why, for example, the lift coefficient at Vr+=1.38, with a considerably lower amplitude than at Vr+=1.18 causes a larger amplitude response. The larger phase angle of the lower magnitude force results in a larger out of phase component than that of the larger force and consequently the work, or energy transmitted to the body is greater which if the damping remains constant eventually leads to a higher response. Figure 10: Lissajou phase diagrams for the different phase of vertical vortex induced response The evolution of the in-phase and out-of-phase components are better studied in the phase plane by means of Lissajou diagrams. The corresponding diagram, for all phases of the build-up, is presented in Figure 11. The hysteric nature of the oscillation cycle is clear in this figure. As can be anticipated, the somewhat elliptical curves are read clockwise, the upper branch corresponding to the loading path. It can be observed how, as the amplitude grows, the phase (the ellipse major axis) rotates from a nearly vertical orientation (force in phase with displacement) to an orientation close to the horizontal (force in phase with the velocity) leading to larger amplitude response. As previously stated that explains how large increases in the displacement follow to lower relative increments in the force magnitude. This could be described as parametric transformation of the ellipse (rotation, scaling and translation). Interestingly, the diagrams do not present any kink as observed in the corresponding cylinder diagram (Blackburn, Govardhan, & Williamson, 2000).

11 The remaining question is how the flow structure around the deck leads to the net forces presented in Figures 9 and 10. The pressure fluctuation on the bottom flange of the leading edge up to the end of the separation bubble are all in phase with the response and therefore do not contribute to the energy transfer or the increase in the response. This can be observed in Figure 11 (left) and will be consistent with the body motion controlling the instability of ISL. Downstream of it, a phase shift is observed in the pressure along the bottom flange Figure 11 (right). The resulting phase with respect to the rotation when the ILEV approaches the trailing edge is 90, which results in optimum contribution to the increase of the oscillations magnitude. This would explain the effectiveness of the guide vanes located around point E. The vanes on the leading edge corner F would distort the structure of the separation bubble and on the trailing edge corner would act complicating the interaction with the body surface as they leave the bottom flange and the consequent out of phase force. Figure 11: Left, pressure coefficients at maximum amplitude oscillation on the lower flange of the leading edge. Constant phase 0. Right, pressure coefficients at maximum amplitude oscillations along the bottom flange, progressive phase shift up to 90º near the trailing edge corner. 4. CONCLUSIONS The vertical vortex induced vibration mechanisms of the Storebælt were investigated. The simultaneously measured pressure field around a section model at the full range of increasing and decreasing wind speeds within the lock-in range was analyzed in detail. Vortex shedding at the trailing edge (TEV) seems to be the only source of significant pressure fluctuation of the motionless deck. The motion induced by these trailing edges vortices may be responsible for the control of the impinging shear layer instability at the leading edge. The onset of the oscillation is therefore attributed to TEV. Significant pressure fluctuations are observed at the leading edge when the motion takes place. The build-up of larger amplitude vibrations appears to be caused by leading edge vortices generated by motion induced instability at the natural frequency. A mechanism that has been referred to as vortex interaction of these vortices and those forming at the trailing edge could be responsible for the enhancement of maximum amplitude oscillations, however this requires further investigation. An increasing phase is observed in the force, with respect to the response, reaching values of /2 consistent with a typical resonant response. Finally it is noted that significant hysteresis behavior is observed in the response.

12 5. ACKNOWLEDGEMENTS The authors gratefully acknowledge the financial support from the University of Western Ontario s Academic Development Fund for the wind tunnel models used in this study. J.M. Terrés-Nícoli acknowledges the support by the GDFA Research Group at the University of Granada. G.A. Kopp gratefully acknowledges the support provided by the Canada Research Chairs Program. 6. REFERENCES Brika, D. a. (1993). Vortex-induced vibrations of a long flexible circular cylinder. Journal of Fluid Mechanics, 250,, Williamson, C., & Govardhan, R. (2004). Vortex-induced vibrations. Annual Rev. Fluid Mech, 36, Zasso, A., Belloli, M., Giappino, S., & Mugiasca, S. (2008). Pressure field analysis on oscillating circular cylinder. Journal of Fluids and Structures, 24, Mills, R., Sheridan, J., & Hourigan, K. (2002). Response of base suction and vortex shedding from rectangular prisms to transverse forcing. Journal of Fluid Mechanics, 461, Parker, R., & Welsh, M. (1983). Effecs of sound on flow separation from blunt plates. International Journal of Heat Fluid Flow, 4, Terrés-Nicoli, J., King, J., & Kim, J. (2007). Wind Effects fot the 3rd Millenium Bridge. 12th International Conference of Wind Engineering (págs ). Cairns: IAWE. Sarpkaya, T. (1979). Vortex Induced Oscillations. Journal of Applied Mechanics, 46, Vickery, B., & Basu, R. (1983). Across-wind vibrations of structures of circular cross-section. Part I. Development of a mathematical model for two-dimensional conditions. Journal of Wind Engineering and Industrial Aerodynamics, 12, Terrés-Nicoli, J., Kopp, G., & King, J. (2003). Mechanisms of the Torsional Vortex Induced Vibration of The Storebaelt Bridge. 11th International Wind Engineering Conference. Lubbock, TE, USA: ICWE. Komatsu, S. a. (1980,). Vortex-induced oscillations of bluff cylinders. Journal of Wind Engineering and Industrial Aerodynamics. 6,, Shirashi, N., & Matsumoto, M. (1983). On classification of Vortex Induced Response and its application for bridge structures. Journal of Wind Engineering and Industrial Aerodynamics, 14, 14, Naudascher, E., & Wang, Y. (1993). Flow Induced Vibrations of Prismatic Bodies and Grids of Prims. Journal of Fluids and Structures, 4, Frandsen, J. B. (1999). Computational Fluid-Structure Interaction Applied to Long-Span Bridge Design.. PhD Thesis. Cambridge University. Frandsen, J. (2001). Simultaneous pressures and accelerations measured full-scale on the Great Belt East suspension bridge. Journal of Wind Engineering and Industrial Aerodynamics, 89, Larose, G. L. (1992). The Response of a Suspension Bridge Deck to Turbulent Wind: the Taut Strip Model Approach. London, ON, Canada: M.E.Sc Thesis. The University of Western Ontario.. Morgenthal, G., & McRobie, F. (2002). A comparative Study of numerical methods for fluid structure interaction analysis in long.span bridge design. Wind and Structures, 5 (2-4), Selvam, R., & Govindaswamy, S. (2001). Aerolastic Analysis of Bridge Girder Section Using Computer Modelling. University of Arkansas. Vezza, M., & Taylor, I. (2003). An Overview of Numerical Bridge Deck Aerodynamics. The QNET-CFD Network Newsletter, 2 (2), Den Hartog, J. (1984). Mechanical Vibrations. Dover Publications Inc. Blackburn, H. M., Govardhan, R., & Williamson, C. (2000). A complementary numerical and physical investigaction of vortex-induced vibration. Journal of Fluids and Structures, 15,