Study On Nonlinear Post-critical Aeroelastic Instability And Self-excited Forces Of Bluff Bodies Of Long-span Bridges

With the bridges advancing towards wide channels and deep mountain gorges,the span record is continually refreshed.The low natural frequency and structural damping,as well as the large angle of attack lead to large challenges of the wind-resistance design for bridges.Traditionary linear theory cannot meet the demands of aeroelastic stability design of super-long bridges.Previous studies indicate that,with the combined effect of structural parameter nonlinearity and aerodynamic self-excited force nonlinearity,a bluff body may suffer ‘soft-galloping’ or ‘soft-flutter’,of which the vibration amplitude increases gradually with respect to the wind speed.This phenomenon brings a new design idea for the aeroelastic stability of super-long bridges.However,the behavior and underlying mechanism of postcritical aeroelastic instability of bridge bluff bodies have not been adequately studied yet,and the calculation method based on nonlinear theory for post-critical aeroelastic instability needs further development.For the sake of further cognition on vibration characteristics and underlying mechanism of post-critical aeroelastic instability of bridge bluff bodies,as well as development of the nonlinear calculation method,the behavior and mechanism of ‘soft-galloping’,torsional ‘soft-flutter’ and coupled ‘soft-flutter’ of bridge structures respectively,the nonlinear self-excited forces,and calculation method for aeroelastic instabilities are systematic studied in this paper.The main contents of this paper are summarized as follows:(1)The aeroelastic instability characteristics and vibration control of main cables of long-span suspension bridges in construction phases are systematically studied.Based on wind tunnel tests of section models,the galloping characteristics,and the effect of structural stiffness,damping,as well as aerodynamic measures on galloping performance of main cables with bluff cross sections are investigated.The effect of self-excited force characterastics on the critical wind speed and vibration amplitude of gal loping are discussed.Results indicate that,the main cables with bluff cross sections have the possibility of suffering soft-galloping at low wind speeds and small angles of attack,and the galloping amplitude increases linearly with respect to the wind speed;nonlinearity of the structural damping cannot obviously affect the galloping amplitude,and the nonlinear aerodynamic self-excited force is the main cause for the linearly increasing of vibration amplitude with the wind speed;due to the strong aerodynamic unsteadiness,the calculation of critical wind speed based on the classical quasi-steady theory has significant error;a combined strategy of using auxiliary ropes to improve structural stiffness,and reducing the spanwise aerodynamic correlation by temporary foamed materials,is proposed for galloping mitigation of actual main cables in construction phases.(2)The characteristics of aerodynamic self-excited forces,as well as the calculation method of galloping amplitude for bluff cross sections of main cables,are studied.Based on FSI(Fluid-structure-interference)simulation through CFD(Computational Fluid Dynamics),the unsteadiness and nonlinearity of self-excited forces as well as its mechanism are analyzed deeply.Besides,a galloping amplitude calculation method based on amplitude-dependent aerodynamic derivatives is developed.Results indicate that,due to the large variation range of effective angle of attack,self-excited forces of the main cable in large-amplitude galloping have remarkable highorder components,and present significant nonlinearity;even at high reduced wind speed(U/f H = 30),the wake flow of the main cable shows significant hysteresis with respect to the cable motion,leading to a significant unsteadiness of the self-excited force;the proposed calculation method for galloping amplitude can reproduce the galloping response obtained through FSI simulation based on CFD,and the effect of structural damping nonlinearity on galloping response can be rapidly and directly predicted by the aerodynamic damping contour.(3)An experimental setup for large-amplitude torsional flutter of section models,as well as a data synchronous acquisition system based on electrical trigger,are developed.The clock-spring-based experimental setup for flutter test are improved: two hinges are installed to the model ends to reduced the friction damping in the ball bellings caused by the bending moment,and both the stiffness and structural damping of the section model are very linear at large vibration amplitudes.Based on the data synchronous acquisition system,the pressure and motion(e.g.,displacement and acceleration)signal of the model can be sampled automatically and synchronously.The reliability of the setup and data acquisition system is verified through the measurement of flutter derivatives of a 5:1 rectangular cylinder.Additionally,the non-wind induced aerodynamic damping of the model in torsional vibration is measured and analyzed.(4)The mechanism of ‘soft-flutter’ and characteristics of aerodynamic self-excited forces of the 5:1 rectangular cylinder are deeply investigated.A series of wind tunnel tests of torsional flutter are carried out on the 5:1rectangular cylinder,in which the aerodynamic pressure and displacement of the cylinder are measured synchronously to obtained the self-excited forces.Based on hysteresis loops of aerodynamic forces,amplitude-dependent flutter derivatives,distribution evolution of fluctuating pressure and aerodynamic power on the cross section,the mechanism of ‘soft-flutter’ and the characteristics of self-excited forces are studied in-depth.Results indicate that,there exist two positive aerodynamic work regions,as well as 1～2negative aerodynamic work regions on both upper and lower sides of the cross section;the phase lag of fluctuating pressure with respect to the motion of the model is crucial for the aerodynamic work contribution of different regions on the cross section.The transient pressure distribution on the vibrating model has significant discrepancy with the mean pressure distribution on the static model with the same effective angle of attack,leading to the strong unsteadiness of the aerodynamic self-excited force.These features of the selfexcited forces suggest that the massive separation associated with the burst of the separation bubbles on the upper and lower sides of the cylinder are significantly delayed due to the torsional motion.(5)A frequency-domain method based on quasi-steady equivalent angle of attack is proposed for galloping/flutter amplitude calculation.Firstly,the static aerodynamic force curves are fitted through 4-order rational fractions,which have an excellent fitting precision compared with traditional high-order polynomials.Then the frequency-domain calculation method based on quasisteady equivalent angle of attack and energy principle is proposed for galloping/flutter amplitude calculation.Results indicate that,the proposed method has conservative calculation results for main cable galloping,which can be used for preliminary prediction of galloping response;concerning bluff body flutter,the calculation results has unacceptable error since the unsteady component of aerodynamic self-excited forces plays a predominant role in post-flutter.(6)Investigation on the combined effect of structural damping nonlinearity and aerodynamic nonlinearity on post-flutter performance of bridge girder is carried out.A streamline box girder under large angle of attack(which is an equivalent bluff body)is taken as the study object,and the‘step-by-step’ flutter calculation method is employed for the calculation of various damping components.The contributions and competitive relations between various aerodynamic and structural damping components are quantified and discussed.Damping contours are obtained and used to predict the post-flutter response(including ‘bifurcation’ and ‘divergence’phenomenon)with different nonlinear structural damping patterns,and the significant effect of structural nonlinearity is clarified.Based on CFD simulation in which the nonlinearity of structural damping is considered,the post-flutter responses obtained through the wind tunnel test and theory calculation are well reproduced.The results indicated that the nonlinear damping can mitigate the “divergence” of flutter amplitude,and increase the security wind speed.