The Reliability Of Vortex Vibration And Flutter Of A Long Span Suspension Bridge With Steel Box Girder

The development of long-span bridges was reviewed,and the research progresses of the wind-induced vibration of long-span bridges,the dynamic reliability and the post-flutter state were introduced in this dissertation.In view of the shortcomings of the current research,deeper researches in these subjects were conducted in this dissertation.For the study of the reliability for vortex vibration and linear flutter,the Gaussian interpolation formula of Gumbel was deduced,and the multiplicative dimensional reduction method(M-DRM)based on the maximum entropy principle has been applied to the reliability analysis of vortex vibration and linear flutter.For the study of the reliability for nonlinear flutter,the nonlinear flutter derivatives were identified based on the CFD numerical simulation with the help of dynamic mesh technique,and the traditional 2D complex mode flutter analysis method has been developed to calculate the critical flutter state and predict the movement in post-flutter state of the main girder.Finally,the the M-DRM and the improved 2D complex mode flutter analysis method were combined to analysis the reliability of nonlinear flutter.The main contents in this paper are as follows:(1)The development of long-span bridges was reviewed,and the state of art of wind engineering was expounded.According to the shortcomings of existing theoretical research,then the research direction and research goal were pointed out.(2)The basic theory and common methods of structural reliability were introduced in this paper,and the defects of existing reliability analysis methods were analyzed.In view of the shortcomings of the existing reliability theory,the Gaussian interpolation formula of Gumbel was deduced,and then it was applied to the M-DRM based on the maximum entropy principle so that the proposed method could be applicated to the wind engineering.To verify the computational accuracy and efficiency of the M-DRM,two numerical examples(explicit limit state function and implicit limit state function)were introduced,and Monte Carlo simulation results were used as the verification criterion.(3)The basic concept of vortex-induced vibration was introduced,and then the vortex respond of section model of a streamlined steel box girder under different wind attack angles(-3~o、0~o and+3~o)was tested in wind tunnel tests.The vortex respond of section model can be conversed to 3D bridge by formula.With the conditional probability,the two failure modes(vortex-induced vibration locked wind speed failure mode and vortex-induced vibration amplitude failure mode)of vortex-induced vibration were comprehensively considered as vortex-induced vibration stiffness failure modes,and the parameters such as wind field characteristics at the bridge position,vortex excitation parameters,Strouhal number and Scruton number were regarded as random variables,then the failure probability of the suspension bridge at each wind angle of attack was solved with M-DRM.(4)The theory of two-dimensional bridge flutter and the identification method of flutter derivatives were reviewed,then the flutter derivatives of the streamlined steel box girder of a long-span suspension bridge are identified by CFD numerical simulation.The flutter deterministic analysis and probabilistic analysis of the suspension bridge were carried out respectively by finite element method and empirical formula method(note:in probabilistic analysis,the finite element method was combined with M-DRM while the empirical formula method was combined with Monte Carlo method).The results show that:in the deterministic analysis,the finite element method is very close to the empirical formula method,and the empirical formula is conservative;in the probabilistic analysis,the results obtained by the two methods are quite different,the error of the two can reach 4.65 times.So the empirical formula method is only applicable to preliminary deterministic analysis.(5)The basic knowledge of computational fluid mechanics was introduced.The nonlinear aerodynamic self-excited force of the streamlined steel box girder was studied with CFD dynamic mesh technique.On this basis,the nonlinear flutter derivatives of the main girder were identified.Based on the 2 degree of freedoms(DOF)coupling flutter theory,the torsional amplitude and the nonlinear flutter derivatives were introduced into the traditional2D complex mode flutter analysis method,and the original program was improved to the“post-flutter state analysis program”so that it can predict not only the critical flutter velocity but also the movement of the girder in the post-flutter state.The post-flutter state includes four stages,namely,“little amplitude zone”,“step amplitude zone”,“linearly growing amplitude zone”and“divergence zone”.Finally,the the M-DRM and the improved 2D complex mode flutter analysis method were combined to analysis the reliability of nonlinear flutter of a long span bridge.