# American Institute of Mathematical Sciences

## 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
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##### References:
Flow chart of vortex-induced vibration analysis method for bridges
The test model and the actual bridge diagram
Electronic pressure scanning valve
Spring in test setup
Spectrum before signal processing
Spectrum after signal processing
Vertical dimensionless amplitude curve with converted wind speed
Frequency of vortex displacement and amplitude spectrum at Vr = 9.837 (+3 deg)
Deduction wind speed Vr = 24.375 vortex displacement time range and amplitude spectrum diagram (+3 deg)
Variation of spreading correlation of lift coefficient with spreading spacing in vortex vibration
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
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°)
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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