索-梁组合结构的建模及面内动力特性分析

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,刚度比和质量比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。

Modeling and In-plane Dynamics Analysis of the Cable-stayed Beam

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 can be 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. The frequency crossover phenomenon is obvious. Considering the local mode and global mode, the mode shapes of the cable-stayed beam are discussed. Finally, the possible internal resonances such as 1:1 and 1:2 are discussed. Researches 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.