Research On Unified Theory And Mechanism Of Nonlinear Wind-induced Static And Dynamic Instability Of Long-span Cable-stayed Bridges

With sustained development of economy of China,the demand of ultra-kilometer cable-stayed bridge is increasingly exuberant.With the continuous increase of cablestayed bridge span,the problem of wind-induced static and dynamic instability has gradually become a controlling factor restricting development,and the classical theory of wind-induced static and dynamic stability is also facing new problems and challenges.With the development of wind-induced aerodynamics and stability theory and the proposal of performance-based wind-resistant design,more and more attention has been paid to the static and dynamic coupling effect and the post-flutter response of bridges.In this context,this paper takes a central-slotted box girder cable-stayed bridge as the research object.Through wind tunnel test,theoretical research and numerical analysis,the static and dynamic coupling effect and wind-induced static and dynamic coupling instability theory of super-long cable-stayed bridge are explored.The main research work and conclusions are as follows:(1)The flutter performance and nonlinear characteristics of the central-slotted box girder section were studied through the wind tunnel test of spring suspension sectional model under attacks of angles(Ao As)of ±10°.It was found that the nonlinear flutter with bifurcation vibration occurred at Ao As of [-4°,0°],and the nonlinear flutter starting from the equilibrium position occurred at Ao As of [-10°,-5°].Flutter did not occur at other angles within the test wind speed range,and flutter performance was good.The two types of nonlinear flutter are heave-torsion coupled flutter.The onset wind speed decreases with the increase of wind attack angle,the steady-state amplitude increases with the increase of reduced wind speed,and the onset amplitude of bifurcation vibration decreases with the increase of reduced wind speed.(2)The general form of coupled flutter displacement signal is discussed.The mode separation method of coupled flutter displacement signal based on Hilbert Transform is proposed,and the influence of mode parameter identification error and noise on mode separation is analyzed theoretically.The modal components separated by mode separation method can be easily processed by equivalent linearization theory and timefrequency analysis theory.Although the mode shape parameter identification error changes the amplitude and phase of the single component signal,it has little influence on the decay rate and frequency.(3)Based on the degrees of freedom balance equation,the free vibration identification method of the amplitude-dependent flutter derivatives was developed.Combined with mode separation method,the amplitude-dependent flutter derivatives can be identified from flutter wind speed range to full wind speed range.Taking the Ao A of-5° of the central-slotted box girder section as example,the identification method was validated and the identification process was illustrated.(4)The full-order polynomial model based on Taylor series expansion is reasonably simplified,and a nonlinear self-excited force polynomial frequency-timedomain model of coupled flutter is proposed.In order to avoid the simultaneous force and vibration measurement test or forced vibration test,an adaptive modeling parameter identification method based on sectional model free vibration test was proposed according to the principle of energy equivalence.The filtering process of adaptive modeling is introduced to determine the orders of damping term and stiffness term.(5)The linear time-domain self-excited force model can’t consider the effect of large additional Ao A and large amplitude on the self-excited aerodynamic force.Therefore,a nonlinear aerodynamic force model based on generalized indicial functions(impulse response functions)in the form of Volterra series is constructed and its applicability under different displacement states is discussed.The static and dynamic coupling effect at the aerodynamic force level is explored through this model.When the mean displacement changes slowly,the effect of the additional Ao A on the aerodynamic force can be regarded as the time-varying effect of the effective Ao A and the corresponding aerodynamic parameters.When the structure moves sinusoidal with large amplitude,the mean term and fundamental frequency term of the aerodynamic force are both affected by vibration amplitude and frequency.The parameter identification of the first order frequency equivalent aerodynamic force are discussed and a time-domain nonlinear model considering the strong wind-induced static and aerodynamic coupling effect is proposed.(6)The concept of three-level coupling effect of wind-induced aerodynamic force,response and instability of wind-induced static and dynamic action of long-span Bridges is proposed,and time-domain unified theory of wind-induced static and dynamic instability of long-span bridges considering wind-induced static and dynamic coupling effect is established and then verified based on the wind tunnel test of a fullbridge aeroelastic model of a cable-stayed bridge with a main span of 1600 m.For general nonlinear systems,vibration affects the mean value of the restoring force and the aerodynamic force,thus affecting the equilibrium position of the structure,and the change of the equilibrium position will affect the vibration of the structure.Therefore,the soft flutter process contains a strong coupling effect between the wind-induced static and dynamic responses,and the vibration and the equilibrium position constantly influence each other.Wind tunnel test and theoretical analysis results show that under the Ao As of-5°,the soft flutter with lateral,vertical and torsional degrees of freedom coupled and wind-induced static and dynamic coupling effect occurs firstly,vertical and torsional mean displacement basically decreases gradually with the increase of torsional amplitude,however,the change of the mean value of lateral displacement is small.(7)The wind-induced static and dynamic coupled instability analysis and parameter analysis of the prototype of cable-stayed bridge with a main span of 1600 m were carried out,theoretical analysis result shows that under the Ao As of 3°,0° and-3°,wind-induced static instability occurs firstly,under the Ao As of-5°,the soft flutter occurs firstly.As the initial Ao A changes from negative to positive,the critical wind speed of wind-induced static instability decreases continuously.The drag coefficient of the cable and the percentage of main beam drag have a great influence on the critical wind speed,while the percentage of lift force and lifting moment of the main beam have relatively small influence on the critical wind speed.The amplitude of considering the coupling effect is smaller than that without considering the coupling effect.With the increase of wind speed,the influence of the coupling effect becomes more and more obvious.