- 學位論文
受地震力作用之斜張橋頻譜分析
Spectral Analysis of Cable-Stayed Bridges under Seismic Loads
摘要
近年來，由於台灣經濟產業快速成長和營建技術大幅提昇，斜張橋被廣泛地應用於橋樑工程，斜張橋結合力學與美學的精髓，兼具超大跨度、造型美觀和建造經濟等優點。然而，這類橋樑具有質量輕、自然頻率低與阻尼低等特性，對於地震十分敏感，因此，地震力為進行斜張橋設計時，必須考慮之重要因素，特別是對位於環太平洋地震帶，震害頻繁的台灣。由此可知，受地震力作用之斜張橋振動特性的探討為一重要課題。本研究接續前人之斜張橋有限元素分析結果，進行受地震力作用之豎琴狀斜張橋單纜索元素系統與多纜索元素系統兩種模型的頻譜分析。使用集集地震垂直與水平方向地表加速度歷時作為地震力，在這兩種地震力作用下，以快速傅利葉轉換為基礎，分別計算豎琴狀斜張橋之節點位移與元素內力的能量頻譜密度函數，進而探討斜張橋動力特性。結果顯示利用節點位移可識別出低頻的整體振態與局部振態，此乃導因於纜索振動過程中，其節點位移變化較元素內力劇烈，因此，利用節點位移可較為有效地識別出各個纜索振動組合而成的局部振態；使用元素內力則可識別出涵蓋低頻與高頻範圍的整體振態與耦合振態，此乃導因於塔樑系統振動過程中，其元素內力變化較節點位移劇烈，因此，使用元素內力識別出之自然頻率可涵蓋較寬廣的頻率範圍，可較為有效地識別出高頻的結構振態。
並列摘要
In the last several decades, cable-stayed bridges have become popular due to their aesthetic appearance, structural efficiency, ease of construction and economic advantage. This type of bridge, however, is light and flexible, and has a low level of inherent damping, resulting in the fact that they are susceptible to seismic loads. Since the geometric and dynamic properties of the bridges as well as the characteristics of the seismic loads are complex, it is necessary to fully understand the mechanism of earthquake-induced vibrations of cable-stayed bridges, which is used to provide the essential information to accurately calculate the dynamic responses of the bridges under seismic excitations. The objective of this study is to present the spectral analysis of cable-stayed bridges under seismic loads. Based on the results of the initial shape, modal and seismic analyses in the previous work, the one-element cable system and multi-element cable system models of the symmetric harp cable-stayed bridge are developed to calculate the power spectral density functions of nodal displacement and internal force using the fast Fourier transform. The findings indicate that the global and local modes in the low frequency range can be successfully captured by the nodal displacement, whereas the global and coupled modes covering a variety of frequency ranges can be efficiently obtained by the internal force.