doi: 10.3934/dcdss.2020262

Spanwise effect of vortex-induced vibration of bridge beam based on symmetric algorithm

School of Highway Engineering, Chang'an University, Xi'an 710064, China

* Corresponding author: Sai Gong

Received  April 2019 Revised  May 2019 Published  February 2020

In view of the problems such as vortex-induced vibration and fatigue of bridge structure caused by wind speed, it is of great significance to study the transverse effect of vortex-induced vibration of the main girder of the main bridge to ensure the safety of the bridge. This paper presents an experimental research method of the spanwise effect of vortex-induced vibration of bridge girder based on symmetric algorithm. The signal amplitude-frequency characteristics of bridge girder are extracted by demodulation method of symmetric differential energy operator. According to this characteristic, a section model of bridge girder is constructed and the correlation between the spanwise effect of vortex-induced vibration and aerodynamic force of the section model of bridge girder is tested. The results show that the structure of main girder is obvious at the angle of attack of +3 and +5 degrees. There are two vertical eddy vibration intervals, and the maximum response of the eddy vibration interval increases with the increase of wind attack angle; with the increase of reduced wind speed, the time history of the eddy vibration displacement of the bridge girder increases and the amplitude decreases; the spread correlation of the lift coefficient for the bridge girder segment model decreases exponentially with the increase of span, and the vortex vibration time gradually increases with the increase of span. It is of great significance to study the vortex-induced vibration of bridge structure effectively and comprehensively, which lays a foundation for studying the spanwise effect of eddy-induced vibration of main girder bridges.

Citation: Sai Gong, Jiawu Li, Peng Tang. Spanwise effect of vortex-induced vibration of bridge beam based on symmetric algorithm. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020262
References:
[1]

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S. W. LiS. Laima and H. Li, Data-driven modeling of vortex-induced vibration of a long-span suspension bridge using decision tree learning and support vector regression, Journal of Wind Engineering and Industrial Aerodynamics, 172 (2018), 196-211.  doi: 10.1016/j.jweia.2017.10.022.  Google Scholar

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W. H. NiuR. Z. Wu and J. L. Chen, Study on vortex force characteristics of bridges based on floating frame force measurement model, Journal of Hunan University (Auto-science Edition), 44 (2017), 135-144.   Google Scholar

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K. Xu and Y. J. Ge, The relationship between bridge section and real bridge vortex-induced resonance amplitude conversion based on wake-oscillator model, Engineering Mechanics, 34 (2017), 137-144.   Google Scholar

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K. XuY. J. Ge and F. C. Cao, Identification of aerodynamic effects of vortex induced vibration on bridge section, Journal of Harbin University of Technology, 49 (2017), 86-92.   Google Scholar

[19]

K. XuL. Zhao and Y. J. Ge, Reduced-order modeling and calculation of vortex-induced vibration for large-span bridges, Journal of Wind Engineering and Industrial Aerodynamics, 167 (2017), 228-241.  doi: 10.1016/j.jweia.2017.04.016.  Google Scholar

[20]

H. F. ZhangD. B. Xin and J. P. Ou, Wake control of vortex shedding based on spanwise suction of a bridge section model using delayed detached eddy simulation, Journal of Wind Engineering and Industrial Aerodynamics, 155 (2016), 100-114.  doi: 10.1016/j.jweia.2016.05.004.  Google Scholar

show all references

References:
[1]

S. J. DanielsI. P. Castro and Z. T. Xie, Numerical analysis of freestream turbulence effects on the vortex-induced vibrations of a rectangular cylinder, Journal of Wind Engineering and Industrial Aerodynamics, 153 (2016), 13-25.  doi: 10.1016/j.jweia.2016.03.007.  Google Scholar

[2]

R. K. EatsonM. J. D. Powell and A. M. Tan, Fast evaluation of polyharmonic splines in three dimensions, IMA Journal of Numerical Analysis, 27 (2018), 427-450.  doi: 10.1093/imanum/drl027.  Google Scholar

[3]

E. D. GedikliD. Chelidze and J. M. Dahl, Observed mode shape effects on the vortex-induced vibration of bending dominated flexible cylinders simply supported at both ends, Journal of Fluids and Structures, 81 (2018), 399-417.  doi: 10.1016/j.jfluidstructs.2018.05.010.  Google Scholar

[4]

F. S. Godeferd and F. Moisy, Structure and dynamics of rotating turbulence: A review of recent experimental and numerical results, Applied Mechanics Reviews, 67 (2016), 030802.  doi: 10.1115/1.4029006.  Google Scholar

[5]

H. Harraga and M. Yebdri, Attractors for a nonautonomous reaction-diffusion equation with delay, Applied Mathematics and Nonlinear Sciences, 3 (2018), 127-150.  doi: 10.21042/AMNS.2018.1.00010.  Google Scholar

[6]

C. N. JiY. Hua and D. Xu, Numerical simulation of vortex induced vibration of flexible cylindrical subjected to flow with different shear rates, Journal of Mechanics, 50 (2018), 21-31.   Google Scholar

[7]

X. Y. Ji, C. Miu and W. Wu, Music symmetric compression spectrum algorithm based on spectral width analysis, Information Technology, 164–168. Google Scholar

[8]

C. G. LiJ. Zhang and Y. B. e. a. Fan, Study of aerodynamic optimization measures for vortex-induced vibration performance of wide streamlined steel box girder, Bridge Construction, 47 (2017), 35-40.   Google Scholar

[9]

S. W. LiS. Laima and H. Li, Data-driven modeling of vortex-induced vibration of a long-span suspension bridge using decision tree learning and support vector regression, Journal of Wind Engineering and Industrial Aerodynamics, 172 (2018), 196-211.  doi: 10.1016/j.jweia.2017.10.022.  Google Scholar

[10]

Z. LiR. K. Jaiman and B. C. Khoo, Coupled dynamics of vortex-induced vibration and stationary wall at low reynolds number, Physics of Fluids, 29 (2017), 093601.  doi: 10.1063/1.4986410.  Google Scholar

[11]

R. F. LiuY. T. Meng and Q. Kang, Influences of converter parameters and modulation methods on common-mode voltage, Journal of Power Supply, 15 (2017), 71-77.   Google Scholar

[12]

W. H. NiuR. Z. Wu and J. L. Chen, Study on vortex force characteristics of bridges based on floating frame force measurement model, Journal of Hunan University (Auto-science Edition), 44 (2017), 135-144.   Google Scholar

[13]

A. Shvets and A. Makaseyev, Deterministic chaos in pendulum systems with delay, Applied Mathematics and Nonlinear Sciences, 4 (2019), 1-8.  doi: 10.2478/AMNS.2019.1.00001.  Google Scholar

[14]

M. G. VisakhA. K. Saha and K. Muralidhar, Effect of spanwise shear on flow past a square cylinder at intermediate Reynolds numbers, Physics of Fluids, 28 (2016), 033602.  doi: 10.1063/1.4943975.  Google Scholar

[15]

E. WangQ. XiaoQ. Zhu and A. Incecik, The effect of spacing on the vortex-induced vibrations of two tandem flexible cylinders, Physics of Fluids, 29 (2017), 077103.  doi: 10.1063/1.4995463.  Google Scholar

[16]

D. B. XinH. F. Zhang and J. P. Ou, Experimental study on mitigating vortex-induced vibration of a bridge by using passive vortex generators, Journal of Wind Engineering and Industrial Aerodynamics, 175 (2018), 100-110.  doi: 10.1016/j.jweia.2018.01.046.  Google Scholar

[17]

K. Xu and Y. J. Ge, The relationship between bridge section and real bridge vortex-induced resonance amplitude conversion based on wake-oscillator model, Engineering Mechanics, 34 (2017), 137-144.   Google Scholar

[18]

K. XuY. J. Ge and F. C. Cao, Identification of aerodynamic effects of vortex induced vibration on bridge section, Journal of Harbin University of Technology, 49 (2017), 86-92.   Google Scholar

[19]

K. XuL. Zhao and Y. J. Ge, Reduced-order modeling and calculation of vortex-induced vibration for large-span bridges, Journal of Wind Engineering and Industrial Aerodynamics, 167 (2017), 228-241.  doi: 10.1016/j.jweia.2017.04.016.  Google Scholar

[20]

H. F. ZhangD. B. Xin and J. P. Ou, Wake control of vortex shedding based on spanwise suction of a bridge section model using delayed detached eddy simulation, Journal of Wind Engineering and Industrial Aerodynamics, 155 (2016), 100-114.  doi: 10.1016/j.jweia.2016.05.004.  Google Scholar

Figure 1.  Flow chart of vortex-induced vibration analysis method for bridges
Figure 2.  The test model and the actual bridge diagram
Figure 3.  Electronic pressure scanning valve
Figure 4.  Spring in test setup
Figure 5.  Spectrum before signal processing
Figure 6.  Spectrum after signal processing
Figure 7.  Vertical dimensionless amplitude curve with converted wind speed
Figure 8.  Frequency of vortex displacement and amplitude spectrum at Vr = 9.837 (+3 deg)
Figure 9.  Deduction wind speed Vr = 24.375 vortex displacement time range and amplitude spectrum diagram (+3 deg)
Figure 10.  Variation of spreading correlation of lift coefficient with spreading spacing in vortex vibration
Table 1.  Vibration parameter table of elastic suspension main beam segment model
Vertical Bend Turn Round
Quality (kg) Frequency (Hz) Damping ratio ($ \% $) Quality moment ($ kg·m^{2} $) Frequency (Hz) Damping ratio ($ \% $)
8.74 4.69 0.326 0.243 9.96 0.225
Vertical Bend Turn Round
Quality (kg) Frequency (Hz) Damping ratio ($ \% $) Quality moment ($ kg·m^{2} $) Frequency (Hz) Damping ratio ($ \% $)
8.74 4.69 0.326 0.243 9.96 0.225
Table 2.  Main beam section model test conditions
Working Condition Flow field state Model state Test content
Working Condition 1 Elastic suspension Synchronize the displacement and surface pressure values of each angle of attack (0°, 3°, 5°) under different wind speeds to identify the vortex locking range
Working Condition 2 Uniform flow field Static state The elastic suspension system is fixed with steel wire to prevent co-vibration. Test the surface pressure values of different wind speeds at different wind angles (0°, 6°, 8°) to study the variation of the model's fixed-time-spread correlation
Working Condition 3 Vibration attenuation Select the representative wind speed point of the vortex vibration range, give the external excitation of the model to attenuate the vibration of the model to the stable displacement value, and record the displacement attenuation curve to identify the vortex excitation force (9°, 11°)
Working Condition Flow field state Model state Test content
Working Condition 1 Elastic suspension Synchronize the displacement and surface pressure values of each angle of attack (0°, 3°, 5°) under different wind speeds to identify the vortex locking range
Working Condition 2 Uniform flow field Static state The elastic suspension system is fixed with steel wire to prevent co-vibration. Test the surface pressure values of different wind speeds at different wind angles (0°, 6°, 8°) to study the variation of the model's fixed-time-spread correlation
Working Condition 3 Vibration attenuation Select the representative wind speed point of the vortex vibration range, give the external excitation of the model to attenuate the vibration of the model to the stable displacement value, and record the displacement attenuation curve to identify the vortex excitation force (9°, 11°)
Table 3.  Spreading correlation analysis of lift coefficient in vortex vibration
Vibration state description First lock zone, vibration point. First lock zone, ascending segment. First lock area, maximum point. First lock zone, descent. First Lock End Point First lock zone, ascending segment. First lock area, maximum point.
wind speed (m/s) 1.73 2.31 2.56 2.66 2.84 5.03 5.84
Vertical dimensionless 0.0003 0.0363 0.0524 0.0505 0.0006 0.0553 0.081
Vertical dimensionless constants 9.3834 11.194 12.4055 12.8901 13.7624 24.3749 28.3001
Vibration state description First lock zone, vibration point. First lock zone, ascending segment. First lock area, maximum point. First lock zone, descent. First Lock End Point First lock zone, ascending segment. First lock area, maximum point.
wind speed (m/s) 1.73 2.31 2.56 2.66 2.84 5.03 5.84
Vertical dimensionless 0.0003 0.0363 0.0524 0.0505 0.0006 0.0553 0.081
Vertical dimensionless constants 9.3834 11.194 12.4055 12.8901 13.7624 24.3749 28.3001
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