斜索-桥面耦合面内参数振动Ⅰ：理论模型

Parametric vibration of inclined cable-deck system Ⅰ:theoretical formulation

斜拉桥拉索具有质量小、阻尼小、刚度小的特点,在外部激励作用下容易产生各种振动,其中拉索在桥面或桥塔的位移激励下的参数振动为主要振动形式之一。考虑拉索垂度、倾角、拉索重力的弦向分力及拉索张力沿索长的变化,将桥面模拟成质量-弹簧系统,建立索-桥耦合振动的两自由度模型,取斜拉索的第一阶模态,采用多尺度法对运动方程进行求解,给出系统在参数共振以及非共振情况下的近似理论解,特别根据理论解得到典型频率处系统响应特征、共振时系统频率匹配关系及振幅发展规律,对于研究索-桥耦合振动这种非线性振动体系的振动特性具有理论指导意义。

Cables in cable-stayed bridges are prone to exhibit transverse oscillation due to their small rigidity, small mass and low damping. The differential equations of the system are established with the consideration of cable sag, cable gravity component in string direction and variation of cable tension along the cable. The Multiple Scale Method is then adopted to derive the close-form formulas of the first modal response of the cable and the bridge deck, and approximate theoretical solutions of the cable in-plane vibration and the deck-equivalent mass are obtained. Specifically, the response characteristics of the cable at typical frequencies are discussed based on the theoretical solutions. The frequency ratios and the amplitude relations between the cable and the deck are deduced when the internal resonances occur.