斜拉桥面内振动的理论建模与特征值分析

Theoretical Modeling and Eigenvalue Analysis on In-plane Vibration of Cable-Stayed Bridges

本文建立了斜拉桥的精细化面内动力学模型,并开展了相应的自振特性分析.首先利用Hamilton变分原理推导了斜拉桥的运动方程,利用边界条件确定了斜拉桥线性化模型的频率方程.然后以双塔三跨斜拉桥为例开展数值分析,通过对比有限元结果验证了数值方法的正确性.同时引入局部化因子定量说明斜拉桥固有模态的特性.最后讨论了不同结构参数、索梁相互作用和结构体系对斜拉桥自振特性的影响.结果表明当系统的固有频率接近纯索频率时,斜拉桥的固有模态将呈现局部特性.同时索梁相互作用明显影响低阶非局部模态,相反可以忽略对高阶固有频率的影响.

In this study,a refined in-plane dynamic model of cable-stayed bridges was constructed,and the corresponding free vibration characteristics were analyzed.Firstly,the in-plane motion equations of the cable-stayed bridge were derived using the Hamilton variational principle,and the characteristic frequency equation of the linearized model was determined based on boundary conditions.A three-span cable-stayed bridge with double towers was chosen for the numerical calculation,and the correctness of the corresponding solution was verified through the finite element method.Then,the modal characteristics of the cable-stayed bridge were quantitatively reflected by introducing localization factors.Finally,the effects of structural parameters,cable-deck interaction,and structural systems on the natural frequencies and modes were discussed.The results show that the natural modes of the system exhibit the local characteristics when the natural frequencies of the cable-stayed bridge are close to the ones of pure cable.Moreover,the cable-deck interaction may significantly affect the low-order non-local modes.However,the effects on the higher-order frequencies can be ignored.