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悬索桥的振动性状中呈现纵飘振动与竖向反对称低阶振动相互耦合的特点。基于挠度理论和能量原理,研究了耦合自振的频率计算方法。首先把加劲梁的单纯纵飘看作单摆振动,得出其等代摆长和振动频率。再结合主缆的竖向反对称低阶振型下的纵向位移特点,建立考虑主缆纵向位移影响的加劲梁纵飘振动的简化计算模型,获得其势能增量的简单表达式。由哈密顿原理,推演了耦合振动频率的计算方法。通过5座桥梁实例验证,利用该文公式获得的耦合频率和振型形状判定与有限元计算结果吻合良好,表明该文提出的计算方法实用可靠。
The vibration characteristics of suspension bridge show the characteristics of longitudinal vibration and vertical antisymmetric low-order vibration coupling with each other. Based on the deflection theory and energy principle, the method of frequency calculation of coupled vibration is studied. First of all, the stiffening girder is considered as a simple pendulum vibration pendulum, draw its equivalent generation length and vibration frequency. A simplified calculation model of longitudinal vibration of stiffening girder considering the influence of longitudinal displacement of the main cable is established based on the longitudinal displacement characteristics of the vertical anti-symmetrical low-order modes of the main cable. A simple expression for the potential energy increment is obtained. By Hamilton principle, deduced the calculation method of the coupling vibration frequency. The results of five bridge cases verified that the coupling frequency and mode shape obtained by the formula are in good agreement with the finite element results, indicating that the calculation method proposed in this paper is practical and reliable.