中文摘要：

研究由弯斜拉桥桥面振动引起的斜拉索参数共振和主共振问题。将弯斜拉桥施工及成桥状态的复杂结构进行简化，建立索-曲梁组合结构力学模型，推导考虑拉索初始垂度及几何非线性影响的索-曲梁组合结构非线性动力学方程。将索与曲梁的连接方式处理为弹性支承。运用多尺度方法研究斜拉索的参数共振和主共振，并对稳态解的稳定性进行分析，同时对斜拉索参数共振和主共振进行数值模拟，得到不同阻尼及不同初始条件下拉索的时间历程曲线。研究结果表明：桥面的低阶振动频率在索的线性振动频率附近且激励幅值在一定范围内时，桥面的小幅振动能够激励起拉索的大幅运动，影响弯斜拉桥施工与运营的安全性。

英文摘要：

The parametric and primary resonances cable-stayed bridge are investigated. The mechanical of stay cables excited by the vibration of deck of curved model of a curved cable-stayed beam is firstly established for research on nonlinear dynamic characters of erection and working stages of the curved cable-stayed bridge. Taking into account the effect of nonlinearity caused by the initial sag, the nonlinear dynamical equation of the curved cable-stayed beam is then obtained. The elastic bearing is applied to deal with the joints between the cable and curved beam. The method of multiple scales is applied to the differential governing equations to analyze the parametric and primary resonances of stay cables. The stability of the steady solutions is also studied. Finally, numerical simulation is used to investigate the parametric and primary resonances of stay cables. The time histories of stay cables under different damps and initial conditions are obtained. The results of numerical simulation show that a small scale vibration of the curved beam may stimulate the cable to undergo large scale movements when the frequency and amplitude of the curved beam within certain scale, it threatens the stability and security in the process of construction and working stage of curved cable-stayed bridges.