| The Π-shaped composite girder has many advantages in engineering application,such as simple appearance,light weight,easy construction,and low engineering cost.It has been widely used in long-span cable-stayed bridges,and has also been used in long-span suspension bridges in recent years.Due to its typically blunt body,the long-span cable-bearing bridges,especially the long-span suspension bridges,with the Π-shaped composite girder is more prone to vertical vortex-induced vibration(VIV)at low wind speed than the streamlined steel box girder.Therefore,it is essential to accurately predict the VIV response of a long-span cable-stayed bridge with the Π-shaped composite girder in order to ensure its operation safety.Though the VIV of a long-span bridge is highly sensitive to structural damping,the influence of structural damping on the VIV response of Π-shaped composite girder is yet not clear,which hinders the accurate prediction of VIV response of the cable-stayed bridge with the Π-shaped composite girder.Based on the wind tunnel sectional model tests and theoretical analysis,this thesis studies the influence of structural damping on the VIV response of the Π-shaped composite girder.The main research contents of this thesis are as follows:(1)A double-side permanent magnet eddy current damper is designed for the large-scale spring-suspended sectional model system firstly.A formula is proposed that relates the additional damping ratio of the spring-suspended sectional model system with the damping coefficient and installation position of the eddy current damper.The most suitable parameters,such as the arrangement of permanent magnets,the geometric dimension and conductivity of the conductor plate are obtained through electromagnetic finite element analysis with the goal to obtain an additional vertical damping ratio not less than 2.0%.Then,a parametric study is performed to detect the influence of air gap size,vibration velocity of the model,and position offset of the conductor on the damping coefficient.Finally,a double-side permanent magnet eddy current damper is manufactured,whose damping coefficient can be accurately and continuously adjusted by variation of the air gap size using a sliding table.(2)Firstly,three additional damping ratio adjustment methods for the spring-suspended sectional model systems are analyzed and compared: winding electrical tapes on the coil spring,installing eddy current damper and tying the wire rope ring on the coil spring.For the method of winding electrical tapes,the dependence of the additional damping ratio on the number of winding turns and position on of electrical tapes is deeply analyzed;for the method of installing eddy current damper,the change of the additional damping ratio with air gap size is measured.Moreover,the reliabilities of these three methods are evaluated by detecting the decay of the additional damping ratio with the excitation number.Then,the effects of the nonlinearity of the structural damping ratio on the lock-in region and the maximum amplitude of the VIV are analyzed by employing the wake oscillator model.At last,a nominal structural damping ratio according to the maximum amplitude of the VIV is proposed to quantify the nonlinear structural damping ratio,and its validity is further demonstrated by a large-scale sectional model wind tunnel test.(3)Firstly,a series of wind tunnel tests are carried out on a large-scale sectional model and a small-scale sectional model to investigate the influence of the structural damping ratio on the VIV response of the Π-shaped composite girder,in which the double-side permanent magnet eddy current damper is used to adjust the additional damping ratio.The influential factors including the attack angle,the aerodynamic measures,geometric scale ratio and the section types are analyzed in the tests.It is found that the variation of the maximum amplitude of VIV with the nominal structural damping is totally different for different sections(means sections with different attack angle,aerodynamic measures or section types),but keep unchanged for different geometric scale ratio.Then,different models of functional relationship between the maximum amplitude of vertical VIV of the Π-shaped composite girder and the Sc number are proposed and compared.At last,a wind tunnel test scheme is suggested,which can balance the prediction accuracy of the maximum amplitude of vertical VIV and number of tests.(4)Based on the wind tunnel test results of the large-scale sectional model,the performances of three different mathematic models of vortex-induced force(VIF)are evaluated: the Scanlan’s empirical nonlinear VIF model,the generalized van der Boer oscillator empirical VIF model and the description function empirical VIF model.The variation of the aerodynamic parameters with the Sc number is analyzed for the above three models,respectively.It is found that the aerodynamic parameters vary significantly with the Sc number for the first two models,while less affected for the last one,which indicates that the description function empirical VIF model has a stronger prediction ability.Finally,for the Scanlan’s empirical nonlinear VIF model and the generalized van der Pol oscillator empirical VIF model,an efficient test strategy for accurately identifying the aerodynamic parameters and predicting the maximum amplitude is proposed. |
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