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中文摘要：
利用哈密顿变分原理以及结构动静态构型的影响，建立了索梁组合结构的约化运动学控制方程．考虑到边界条件和耦合连接条件，我们研究了体系的面内特征值问题．根据求解得到的面内特征值方程，并通过分段函数的引入，结构的模态函数可以被直接确定．随后，我们研究了参数垂跨比f，刚度比K和质量比m对面内固有频率的影响．研究发现从结构的频率谱图中可以看出频率跳跃现象是存在的，另外，频率穿越现象也是十分明显．随后，考虑到局部模态和整体模态，结合之前确定的特征值方程及分段振型函数，我们研究了索梁组合结构可能的模态形状．最后，我们讨论了索-梁组合结构可能发生的内共振形式，比如面内1：1内共振形式以及1：2内共振形式．研究表明梁的静态构型不仅直接影响到耦合力连接条件，还将影响索-梁组合结构频率的确定．
英文摘要：
Using the Hamilton principle and the effects of the dynamic and static configuration of the cable and beam, the equations of motion of the cable-stayed beam can be obtained. Considering the boundary and continuity conditions, the in-plane eigenvalue problem is investigated. By introducing the piecewise function,the mode shapes is obtained. Then, the effects of the sag-to-span ratio f, stiffness ratio K and mass ratio m on the in-plane natural frequencies of the cable-stayed beam are studied. It is shown that the curve veering phenomenon can be observed in the natural frequency spectrum of the system, and the fre- quency crossover phenomenon is obvious. By taking the local mode and global mode into account, the mode shapes of the cable-stayed beam are discussed. Finally, the possible internal resonances such as 1 ： 1 and 1 ： 2 are further discussed. Our results clearly show that the static configuration of the beam influences not only the force continuity conditions, but also the natural frequency of the cable-stayed beam.
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