1.

INTRODUCTION

When the airflow passes around an object, periodic shedding vortices will be generated on both sides of the object and in the wake. This periodic excitation causes the object to undergo limit-cycle vibrations known as vortex-induced vibrations^1,2. These vibrations typically occur at lower wind speeds and are usually in the form of vertical vortex-induced vibrations and torsional vortex-induced vibrations. Single cable suspensions, due to their large span, low torsional stiffness, and low damping, are sensitive structures to wind-induced responses and are prone to vortex-induced vibrations^3,4. Based on Yinghua Bridge, this paper researches the characteristics of vortex-induced vibrations in single-main-cable bridges and proposes measures to mitigate vortex-induced vibrations through wind tunnel tests. The bridge spans of the Yinghua Bridge are arranged as follows: 45m+410m+45m, with a total length of 500m. The girder adopts a streamlined box girder section, with six lanes in both directions. The bridge deck is 37.8 m wide, and the pylons are designed in a unique curved shape, as shown in Figures 1 and 2. The design basic wind speed at the bridge site is 25.6 m/s. The area where the bridge is located has open water surfaces, with ground roughness classified as Type B, and an average wind speed profile index of 0.16.

Figure 1.

Rendering of Yinghua Bridge.

Figure 2.

Layout of standard cross-section for Yinghua Bridge

This paper adopts a segmental model test to measure the wind speed of vortex-induced vibrations, maximum amplitude, and Strouhal number of main girder section, thus makes an assessment of vortex characteristic of the girder, and proposes measures to suppress vortex-induced vibrations of the girder if necessary.

2.

WIND TUNNEL TEST ON VORTEX INDUCED VIBRATION

The vortex-induced vibration test model of the Yinghua Bridge is suspended on supports by eight tension springs (Figure 3). Since the occurrence of vortex-induced vibration does not depend on the bending-torsion coupling mechanism, there is no requirement for the ratio of torsional to bending frequency of the model system. Due to the fact that vortex-induced vibration typically occurs at lower wind speeds, in order to reduce the model’s wind-speed ratio, stiff springs are used to increase the model’s natural frequency^6,7. The test simulated both the completed bridge state and the 100% construction state. The damping ratios for the test were set at 0.3% and 0.5% respectively. The model scale ratio is 1:50.

Figure 3.

Model of vortex-induced vibration wind test section of Yinghua Bridge.

The vortex-induced vibration test model was tested at five different angles of attack: α=0°, +3°, -3°, +5°, and -5°. The tests were conducted in a uniform flow field. For each model condition, the test wind speed ranged from 1 m/s to 18 m/s, increasing by 0.2 m/s. Once the vortex-induced vibration region was identified, the wind speed was then increased by 0.1 m/s to determine the accurate vortex-induced resonance starting wind speed and maximum amplitude. Laser displacement sensors were used during the test to measure the real-time displacement response at the edge and middle position of the main beam, thereby obtaining the vertical displacement and torsional displacement of the model.

According to the Wind-resistant Design Specification, the allowable amplitudes for the first-order symmetric vertical bending and torsional vortex-induced resonance in the completed state of the Yinghua Bridge are as follows:

where f_h and f_α are vertical and torsional fundamental frequencies, respectively, can be determined through finite element analysis. B is the width of the bridge deck.

3.

VORTEX-INDUCED VIBRATION TEST RESULTS OF THE ORIGINAL DESIGN SCHEME OF YINGHUA BRIDGE

Figure 4 displays the vertical and torsional wind-induced vibration curves. According to relevant regulations for bridge traffic in China, when the wind speed exceeds 25 m/s, bridge traffic is restricted. Therefore, the focus of this bridge is on addressing vortex-induced vibrations occurring at speeds below 25 m/s. The test results indicate that in the completed state of the bridge, significant vertical and torsional vortex-induced vibration phenomena were observed at 0° and +3° angles of attack. The vortex-induced vibration phenomena at +3° angle of attack were particularly severe, far exceeding the allowable amplitude in the regulations. Consequently, the vortex-induced vibration performance of the bridge does not meet the standards and requires aerodynamic optimization based on the specific conditions of the bridge. This optimization aims to eliminate the potential danger of vortex-induced vibrations through wind tunnel tests.

Figure 4.

The curve of the amplitude with wind speed of the original grid section.

4.

RESEARCH ON VORTEX-INDUCED VIBRATION SUPPRESSION FOR YINGHUA BRIDGE

Seven vibration suppression schemes have been proposed to mitigate or reduce the amplitude of the vortex-induced vibrations. Segment model tests were conducted for each scheme to identify the optimal vortex-induced vibration suppression solution^8-10. In this experiment, two sets of damping systems were utilized, with vertical and torsional damping ratios of ξ=0.30% and ξ =0.50%, respectively. Since the use of relatively small damping ratios in the experiment tends to be safer compared to actual bridge conditions, the evaluation of the test results in this paper is based on the first-order vertical and first-order torsional. The optimization scheme is described as follows:

In optimization plan 1, the position of the guide rail remains unchanged, while a flow deflector is added behind the guide rail, with the other structure unchanged, as shown in Figure 5a.

Figure 5.

Optimization plan.

In optimization plan 2, the position of the guide rail remains unchanged, while a flow deflector is added behind the guide rail, and aerodynamic wing flaps are added to the railing. The other structure remains unchanged, as shown in Figure 5b.

In optimization plan 3, the position of the guide rail remains unchanged, while a flow deflector is added behind the guide rail. The outer edge of the pedestrian walkway slab is modified to be sloped, aligning with the slope of the wind mouth on the same plane, with the remaining structure unchanged, as shown in Figure 5c.

In optimization plan 4, the upper edge of the wind mouth is aligned with the surface of the pedestrian walkway slab, and the wind mouth is streamlined (referred to as a large wind mouth in this paper), with the remaining structure unchanged, as shown in Figure 5d.

In optimization plan 5, a large wind mouth and a flow deflector behind the guide rail were used, the remaining structure unchanged, as shown in Figure 5e.

In optimization plan 6, the dimensions of the original wind mouth are adjusted to streamline it further (referred to as a small wind mouth in this report), with the remaining structure unchanged, as shown in Figure 5f.

In optimization plan 7, a small wind mouth and a flow deflector behind the guide rail were used, and the pedestrian walkway slab was removed, with the remaining structure unchanged, as shown in Figure 5g.

The wind-induced vibration curve for optimization schemes 1-7 is shown in Figure 6. From the figure, when the wind speed is within 25 m/s, the amplitude of vortex-induced vibration is as follows: in optimization plan 1, plan 3, and plan 4, at a +3° angle of attack, the vertical bending amplitude exceeds the allowable amplitude, while the torsional amplitude is less than the allowable amplitude. In optimization plan 2, plan 5, plan 6, and plan 7, at +3° angle of attack, both the vertical bending and torsional amplitudes are less than the allowable amplitude.

Figure 6.

The curve of the amplitude with wind speed of optimization plan.

5.

CONCLUSION

Through the aeroelastic vibration test of the main beam segment model, it is found that severe aeroelastic vibration phenomena occur in the original main beam design at 0° and +3° attack angles. Through a series of cross-section optimization tests, it was discovered that both optimization scheme 6 and scheme 7 can eliminate aeroelastic vibrations and torsional vibrations at low wind speeds. Even with 0.3% low damping and +5° situation, the design meets the specifications with sufficient margin. Considering that the bridge is a municipal bridge with high aesthetic requirements, scheme 6 is more suitable for the Yinghua Bridge.

Single-main-cable suspension bridge is prone to vortex-induced vibration, especially vertical vortex-induced vibration, which occurs at a relatively lower wind speed and directly affects the service performance of the bridge. The torsional frequency of a single-main-cable suspension bridge is relatively low, and torsional vortex-induced vibration may also occur at a relatively low wind speed. Both types of vortex-induced vibration are issues that need special attention in the design of single-main-cable suspension bridges. The test results show that through the aerodynamic optimization of the main girder, without changing the main features of the main girder, by changing the guardrail or wind deflector, the vortex- induced vibration of the single-main-cable suspension bridge can meet the design requirements.