Numerical Simulation Of Flutter Performance Of Long-span Bridges

For long-span flexible bridges,flutter is the most dangerous wind-induced divergent vibration,which should be strictly prohibited.The numerical simulation on wind-induced response of bridge structures is reviewed,and the current research on the identification techniques of flutter derivatives and flutter analysis of bridge structures is summarized.Aiming at the existing problems and defects,the present numerical study will focus on the identification of flutter derivatives,parameter analysis of flutter derivatives,nonlinear characteristics of self-excited force,nonlinear aerodynamic effect under zero wind speed,divergent flutter performances and limit cycle flutter performances.The major researches and conclusions are as follows:(1)The 3-DOF coupled forced vibration numerical method for extracting aerodynamic derivatives of deck sections is firstly proposed.Flutter derivatives of thin plate section and typical deck sections are numerical identified.Reasonable agreements between results from present numerical method and those from theoretical solution or wind tunnel tests demonstrate the reliability and efficiency of coupled numerical technique.The proposed coupled numerical method can provide almost the same level of accuracy as the 1-DOF method and saves about 67%of the computation time.A numerical method,exponential attenuate/divergent forced vibration method for investigating the influence of damping ratio and amplitude on flutter derivative,is proposed.The flutter derivatives of thin plate section and bluff deck section under different damping ratio and amplitude are simulated.The results show that the damping ratio and amplitude have influences with different degrees on flutter derivative.The proposed method provides a more efficient and effective method for parameter analysis of flutter derivative.(2)The nonlinear characteristics of self-excited forces are studied using harmonic analysis,and the aerodynamic derivatives are proved to be immune to the high-order components mathematically.The results show that the self-excited drag contains remarkable high-order harmonic components,and the linear model would no longer be applicable.The appropriateness of the modal superposition assumption for the self-excited forces generated by different motions is also examined.A nonlinear mathematical model,which could characterize both first-and high-order components,is developed,and the corresponding lateral flutter derivatives are identified.The self-excited drag forces of four typical deck sections during vertical,lateral and torsional vibration are numerically simulated,and the efficiency of present nonlinear model is verified.The numerical simulation results indicate that the nonlinear features of self-excited drag forces mainly depending on the aerodynamic configurations,and the symmetry of deck section about its horizontal axis is the key factor for determining the proportion of high-order harmonic components.(3)Based on weak coupling,the numerical model for simulating the wind-induced vibration of bridge structure is developed.The mathematical expression of the aerodynamic forces for vibrating deck section under zero wind speed is proposed.The free vibration responses of thin plate section and bridge deck section at zero wind speed are numerically simulated,and then the nonlinear vibration frequencies and damping ratios are calculated.The results indicate that the aerodynamic effect of deck section during vertical and torsional vibration cannot be neglected,otherwise the error will be increased.(4)The vibration response and critical flutter state of thin plate section and streamlined deck section are numerically simulated.The critical flutter speed and flutter frequency obtained by present simulation agree well with the theoretical solution and experimental results.The lateral deviation characteristics of aerodynamic torsion center of deck section during flutter are analyzed.The driving mechanism of divergent flutter is examined from the viewpoint of energy transfer of deck section during vibration.The airflow energy input characteristics at different position of deck section during flutter are further analyzed.The results indicate that due to the coupled bending-torsional effect,the position of aerodynamic torsion center periodically changes when flutter occurs.Whether the effective work done by aerodynamic force is positive or negative is mainly determined by the phase angle between the displacement and aerodynamic force.Due to the generation of separated vortex and shift of stagnation point on windward side,the energy absorbing region of deck surface increases significantly with the increase of amplitude during divergent flutter.(5)The limit cycle flutter(LCF)responses of streamlined deck section under different initial attack angles and inlet wind speeds are simulated.The influences of lateral DOF,structural damping and initial excitation on the LCF response are investigated.The results indicate that with the increase of attack angle,the deck section becomes much blunter,which leads to be more prone to LCF.The lateral DOF has little effect on LCF responses.The structural damping has remarkable influence on the LCF critical wind speed and the amplitude.The steady-state responses of LCF are independent of the initial excitation conditions.(6)The nonlinear and hysteresis characteristics of aerodynamic forces of deck section during LCF are discussed.The harmonic analysis of fluctuating pressure at different position of deck surface is conducted.The driving mechanism of LCF is examined from the viewpoint of energy transfer of deck section during vibration.The simulated results indicate that the aerodynamic forces and displacement of deck section consists of several harmonic components,whose frequencies are integer multiples of fundamental frequency.The work done by aerodynamic force is mainly contributed by fundamental harmonic component.The phase angle between the displacement and aerodynamic force changes with the amplitude and decides the trend of the effective work done by aerodynamic force in one cycle.LCF occurs when the aerodynamic work done by air flow on the deck section is equal to the dissipated energy by structure damping.