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利用非线性理论和混沌时间序列分析方法,建立了桥梁风致振动的数学模型,开发了计算桥梁振动加速度时间序列Lyapunov指数的MATLAB程序,进行了桥梁涡振和颤振的风洞试验,分析了不同风攻角下的桥梁风致振动的阻尼比、Lyapunov指数与风速的关系以及涡振振幅与风速的关系,研究了桥梁颤振和涡振的混沌特性。试验结果表明:在颤振试验中,当风速小于颤振临界风速15.5m·s-1时,Lyapunov指数小于0,Lyapunov指数与阻尼比存在很大的相关性,当风速从3m·s-1增大为18m·s-1时,相空间逐渐发散;在涡振试验中,当风速从4.5m·s-1增大至8.5m·s-1时,Lyapunov指数大于0,桥梁发生明显涡振,并由多频振动逐渐转变为单频振动,相空间变为一个较为理想的圆。桥梁的涡振与颤振均属于混沌现象,低风速下的Lyapunov指数可用来预测高风速下的风致振动,并且利用相空间也能识别涡振与颤振。
Using nonlinear theory and chaotic time series analysis method, the mathematical model of wind induced vibration of bridge is established. The MATLAB program of calculating Lyapunov exponent of bridge vibration acceleration is developed. The wind tunnel test of vortex and flutter is carried out. The wind-induced damping ratio of the bridge under wind-attack angle, the relationship between the Lyapunov exponent and the wind speed, the relationship between the amplitude of the vortex and the wind speed, and the chaotic characteristics of the flutter and vortex of the bridge are studied. The experimental results show that the Lyapunov exponent is less than 0 when the wind speed is less than the critical flutter speed of 15.5m · s-1, and the Lyapunov exponent has a great correlation with the damping ratio. When the wind speed is from 3m · s-1 When the wind speed increases from 4.5 m · s-1 to 8.5 m · s-1, the Lyapunov exponent is larger than 0 and the vortex is obviously vortex Vibration, and multi-frequency vibration gradually into single-frequency vibration, phase space into a more ideal circle. The vortex and flutter of bridge all belong to the chaos phenomenon. The Lyapunov exponent at low wind speed can be used to predict the wind-induced vibration under high wind speed, and the vortex and flutter can also be identified by using the phase space.