协作体系斜拉桥竖向自由振动理论研究

Theoretical study of vertical free vibration of collaborated system cable-stayed bridge

基于大位移非线性弹性理论的广义变分原理,考虑加劲梁轴向压缩应变能和剪切应变能的影响,建立了协作体系斜拉桥空间耦合自由振动的大位移不完全广义势能泛函,通过约束变分导出了协作体系斜拉桥的加劲主梁竖向挠曲振动微分方程.同时以金马大桥为例,构造了T构与斜拉桥协作体系的边界条件.求解出的竖向振动方程的解析解,与有限元数值结果对比吻合良好,证明了方法的正确性.这一方法可为同类型结构的固有振动特性分析提供参考.

Based on the generalized potential variational principle of nonlinear elasticity theory with large deflection, the incomplete generalized potential energy functional with large deflection is established on the space coupling free vibration of collaborated system structure by considering the effect of axial compressive and shearing strain energy of stiffening girder. By constraint variation, the differential equations of vertical vibration of the stiffening girder of collaborated system cable-stayed bridge were derived. The Golden Horse Bridge with T-shape rigid structure and single-tower cable-stayed bridge is taken as an example for the solution of vertical vibration differential equation through the presented boundary condition. By comparing with finite element numerical results the correctness of the method is testified, and the method can provide more attention to the analysis of free vibration of this kind of structure.