模态跃迁下斜拉桥的风/雨激振研究

Dynamic analysis of rain/wind-induced vibration of cable-stayed bridges is one of hotspots and hardest work in the areas of bridge engineering in recent decades.The current study focus on the parametric vibration, or rain/wind-induced vibration of inclined cables of cable-stayed bridges. On the other hand, there is little research on the influence of moving vehicles, variation of parameters, or rain upon cable-stayed bridges. In this proposed project, cable-stayed bridges, which are regarded as complex multi-flexible bodies, are dynamic modeling using continuous models, and the rain/wind-induced vibration is studied in view of mode jumping. The main contents of this project are given as following: (1)Repeated natural frequencies, and close natural frequencies of cable-stayed bridges are studied using the group presentation theory which is usually compatible to discretized dynamic systems; (2) The specific patterns of mode jumping of cable-stayed bridges and their mechanism are revealed using matrix perturbation methods which are usually compatible to discretized dynamic systems, and experimental work is carried to velidate the theoretical prediction; (3) Dynamic analysis of cable-stayed bridges induced by rain/wind are studied, which are considered the influence brought by the mode jumping. Mode jumping resulted from the moving vehicles, and the ununiform distribution of rain on the cables as two situations are studied, respectively.This project will serve for many aspects related to the structural design, the fast reanalysis of structures, the damage detection as well as vibration control for cable-stayed bridges.

斜拉桥的风/雨激振问题是近几十年来桥梁工程领域的热点和难点问题之一。目前的研究主要针对拉索参激振动或风/雨等外激振动，分析过程中很少考虑到移动车辆、斜拉桥结构参数变化、雨水附加质量等对斜拉桥固有特性的影响。本项目将斜拉桥当作多个细长柔性体组成的复杂系统，在连续体系统的框架下，从模态跃迁的角度对斜拉桥的风/雨激振进行研究，主要内容包括：（1）探讨斜拉桥出现重频、密频的机理，研究群表示理论在连续体系统中的应用问题；（2）揭示斜拉桥独有的模态跃迁模式并探讨其机理，研究矩阵摄动法在连续体系统中应用的问题，并设计相应的实验进行验证；（3）分别分析移动车辆以及雨水引发的模态跃迁对斜拉桥风/雨激振行为的影响，深入揭示斜拉桥丰富的非线性动力学行为。本项目将为斜拉桥的结构设计、结构快速重分析、损伤检测、振动控制等提供理论服务。

本研究系统地探讨了斜拉桥的自由振动、车桥耦合振动、涡激振动以及考虑模态跃迁时的涡激振动等动力学问题。采用连续体系统建模方法对斜拉桥进行了建模，通过Galerkin方法求解斜拉桥的强迫振动问题。采用切换系统对考虑模态跃迁下斜拉桥的涡激振动进行建模，结合时间历程图、相图、Poincare截面等方法分析其复杂的非线性动力学行为。数值结果表明：整体对称性以及局部对称性斜拉桥都存在模态跃迁、频率曲线偏转、密集固有频率、模态局部化现象；Galerkin方法求解车桥耦合问题时，需要截取前49阶模态。然而在这些模态中，只有少数几阶模态起主要作用；密集频率与模态局部化现象对车桥耦合问题具有显著的影响；斜拉桥的涡激振动具有多个稳定的极限环。斜拉索的几何非线性可导致斜拉桥涡激振动出现混沌解；振动过程中反复出现的模态跃迁行为会给斜拉桥的涡激振动带来更为丰富的非线性动力学行为。该研究可为斜拉桥的初始设计与振动控制提供理论依据。