Tuned Mass Damper Control Of Vortex-Induced Vibration In The Hong Kong-Zhuhai-Macao Bridge Deep-Water Non-Navigable Bridge

When the wind flows past a bridge deck,the periodic vortex-shedding occurs and then causes the bridge deck experience a vortex-induced vibration(VIV)with a vertical bending mode or torsional mode.If the vortex shedding frequency approaches to a natural frequency of the bridge deck,the bridge deck will experience a vortex-induced resonance.Although the resonance is not catastrophic as the flutter,it greatly impacts serviceability and driving comfort due to the high likelihood and large amplitude.The tuned mass damper(TMD)is widely used to mitigate the VIV in bridges through absorbing and dissipating the vibration energy from the bridge.However,the parameter design,control effect evaluation,stroke limitation,and robustness of the TMD have not been well studied due to ignoring the nonlinearity and uncertainty of the VIV.Taking the Hong Kong-Zhuhai-Macao Bridge Deep-Water Non-Navigable Bridge as the engineering object,this thesis investigates the VIV mitigation using the TMD.Wind tunnel tests showed that the bridge will experience a large-amplitude vortex-induced resonance with the first vertical bending mode within design wind speeds,and the TMD scheme was adopted for VIV mitigation.Based on the robustness,a design framework of the TMD control,including the parameter design and control effect evaluation,is proposed.Furthermore,a novel viscoelastic TMD is proposed to improve the VIV mitigation of the bridge,and corresponding experimental and theoretical studies are performed.The main research work and conclusions are listed below:(1)The VIV mitigation of the Hong Kong-Zhuhai-Macao Bridge Deep-Water Non-Navigable Bridge using the TMDWind tunnel tests of the Hong Kong-Zhuhai-Macao Bridge Deep-Water Non-Navigable Bridge showed that the girder will experience a vertical vortex-induced resonance with 150 mm amplitude when the wind speed is between 27 m/s and 35 m/s,and TMDs are used to mitigate this VIV.The equivalent damping ratio contributed by TMDs is derived using the Krylov Bogoliubov method,and it depends on the TMD parameters,which influence the vortex-induced resonance frequency.The vortex-induced amplitude is sensitive to the aerodynamic parameters,while the equivalent damping ratio is sensitive to the modal parameters of the bridge.Three typical design formulas for the TMD are compared based on the proposed probability of failure.Filed test results showed that the damping ratio of the first mode of the bridge is improved from 0.65% to 2.11% after installing TMDs.(2)Performance tests of the viscoelastic TMDThe configuration and energy consumption principle of the viscoelastic TMD are introduced.The mechanical performance tests of main components are performed.Test results showed that the natural frequency and damping ratio of the cantilever beam can be adjusted by changing the lumped mass position and viscoelastic layer thickness.The larger the steel ball radius,or the thinner the viscoelastic layer,or the greater the collision velocity,the smaller the coefficient of restitution of the viscoelastic layer-steel collision.The viscoelastic TMD can effectively suppress the free vibration both in the well-tuned and mis-tuned cases.(3)Mechanical model of the viscoelastic TMDAccording to the Oberst beam theory,the viscoelastic cantilever beam can be considered as a homogeneous beam with a sectional complex stiffness.The proposed mechanical model based on the energy theory can be used to estimate the modal parameters of the viscoelastic cantilever beam with a lumped mass.The proposed strategy based on acceleration measurements can identify the pounding stiffness of the viscoelastic layer-steel collision.The identified Hunt-Crossley model can be applied into the viscoelastic TMD control,and the simulation results are basically consistent with the experimental results.(4)The vibration suppression analysis of the viscoelastic TMD.The equations of motion of the structure-viscoelastic TMD system in the three working modes are established.Numerical simulations of the structure-DTMD,pounding TMD,and viscoelastic TMD systems under the harmonic force were performed,respectively.The analysis indicates that the secondary TMD in the DTMD plays a role as the damping element in the TMD;there is an optimal proportion between the tuning and collision in the pounding TMD;the effectiveness of the viscoelastic TMD decreases with the decrease in the gap,but the robustness and stroke limitation are improved.(5)The VIV mitigation of the Hong Kong-Zhuhai-Macao Bridge Deep-Water Non-Navigable Bridge using the viscoelastic TMD.The equations of motion of the bridge-multiple viscoelastic TMD system under the VIV are established.The equivalent damping ratios contributed by the MDTMD or MTMD are derived using the Krylov Bogoliubov method.The result shows that the MDTMD and MTMD have better robustness than the DTMD and TMD.The viscoelastic TMD is used to mitigate the VIV in the Deep-Water Non-Navigable Bridge.The numerical results show that the viscoelastic TMD has larger equivalent stiffness and damping due to the collision than the TMD.The smaller the gap,the more violent the collision,the smaller the optimal frequency ratio.The control effect of the viscoelastic TMD is still dominated by the tuning,supplemented by the collision in the VIV mitigation.The single or multiple viscoelastic TMD has better control effect and stroke limitation than the single or multiple TMD in the mis-tuning cases.The innovations of this paper are listed below:(1)A novel viscoelastic TMD with multiple energy consumption modes is proposed to mitigate the VIV in the Hong Kong-Zhuhai-Macao Bridge Deep-Water Non-Navigable Bridge,and its better control robustness and stroke limitation capability than the TMD are validated by numerical simulations.(2)According to the damping ratio contributed by the TMD and the aerodynamic parameters identified from wind tunnel tests,a probability of failure for the VIV mitigation of long-span bridges is proposed.Based on the probability of failure,the TMD parameters can be well optimized and control effect can be reasonably evaluated.(3)The damping ratio contributed by multiple viscoelastic TMDs are proposed.Based on this damping ratio,the parameter optimization of multiple viscoelastic TMDs are performed,and the time-domain simulation of the long-span bridge with multiple viscoelastic TMDs under the VIV is performed to validate the optimal viscoelastic TMD.