斜張橋纜索在車行載重下之振動分析

Vibration Analysis of Cables in Cable-Stayed Bridges due to Moving Loads

陳立人(Li-Jen Chen)

指導教授 ： 楊永斌

國立臺灣大學/工學院/土木工程學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.02021

摘要

纜索在斜張橋的承載機制中，扮演著不可或缺的角色。但出乎意料地，斜張橋纜索在車行載重下的振動問題，或可以更精確地說，由支承運動所引致的纜索振動問題，卻很少成為學者研究的題材。唯近年來釵h工程師常發現，有時即便是在微風且車流量少的情況下，某些特定纜索的振動量竟然大到可以破壞錨定端的披覆材料，此一現象使得纜索振動的問題逐漸受到世人的重視。為了進一步分析纜索振動的問題，在考慮纜索的撓曲勁度下，本文根據受初始張力下纜索的振動方程式，推導出由支承運動而引致纜索振動的解析解。在假設支承運動可經由有限元素法事先分析橋樑求得的情況下，此解可以進一步地推廣至分析斜張橋的纜索振動問題。
傳統上由於缺少一有效分析纜索振動的方法，使得纜索佈置的選擇多取決於美觀考量，鮮少考慮其相對應纜索的動力特性。為了彌補這缺憾，本文將依前所提的纜索分析方法，來探討不同的纜索佈置，對於纜索振動的影響。此外，本文亦會探討斜張橋纜索在斜張橋受序列載重下的動力特性。而由本文的分析可發現，由於斜張橋是一相當複雜的結構系統，有可能因為纜索頻率與橋梁或驅動頻率之間的重合或接近，而造成纜索振動反應被放大的情形。本文各項分析所得的結果，應有助於解釋並進一步減少斜張橋纜索的振動。

關鍵字

斜張橋 ； 共振 ； 撓曲勁度 ； 車橋互制 ； 振動 ； 纜索 ； 纜索佈置

並列摘要

Cables play an important role in the load-carrying system of cable-stayed bridges. Surprisingly, the problem of vehicle-induced vibration of cables mounted on cable-stayed bridges or, specifically, the problem of cable vibration induced by support motions, received only very limited attention from researchers. Based on the governing differential equation of a cable with initial tension, an exact solution was derived for the cable with support motions, considering the contribution of flexural rigidity. Such a solution is then extended to the analysis of vibration of cables mounted on a cable-stayed bridge under the moving loads, with the support motions of the cables made available by a finite element analysis carried out in advance for the entire bridge.
Conventionally, the arrangement of cables is chosen primarily based on the aesthetic considerations, while the corresponding dynamic property of the cables is seldom considered, partly due to the lack of a simple approach for analyzing the cable vibrations. To fill the gap, the influence of arrangement of cables on cable vibration will be investigated in this study, based on the proposed analysis procedure. Furthermore, the dynamic behavior of cables in cables-stayed bridges under serial moving loads will also be studied, from which it is concluded that the responses of cables in cable-stayed bridges will be amplified, when the frequency of the cable concerned coincides with any of the bridge or excitation frequencies. The results presented herein are useful for the design of bridges aimed at reducing the cable vibrations.

並列關鍵字

cable ； cable arrangement ； cable-stayed bridge ； resonance ； vehicle-bridge interaction ； flexural rigidity ； vibration

參考文獻

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