臺灣博碩士論文加值系統

摘要
本文主要研究高速列車通過橋梁時的車橋互制反應，特別考慮橋梁的扭轉效應，藉以探討高速列車通過橋梁時的
垂直振動和扭轉振動反應；並變化不同的車體參數，以此分析不同車體參數對車橋互制問題的影響。
本文以自行建立的有限元素程式，利用Newmark-β有限差分將車體自由度濃縮至橋梁上，推導出三維RVBI元素，
可作高速列車行駛時，作用點不在橋梁中心所造成的垂直振動和扭轉振動之問題分析及研究。
由研究結果顯示，當一列的高速列車通過橋梁時，當其營運速度會激發橋梁的扭轉共振速度時，橋梁扭轉角會漸變大而發散，故在高鐵設計上，列車營運速度應避開會使車體發生共振的速度。

第一章 導論…………………….…………………..…1
1.1 研究動機與目的.....……………………….1
1.2 文獻回顧………………………….....……2
1.3 研究範圍…………………...………......5
第二章 直梁的有限元素推導.....……………………….…7
2.1 前言…………………………….....….….7
2.2 直梁元素…………………… ..……..7
2.3 直梁運動方程式………....……………….10
2.4 直梁元素的諧和質量矩陣、彈性勁度矩陣
及系統阻尼矩陣..........………………………12
2.5 直梁元素的諧和節點力…….…………....15
2.6 系統運動方程式…………………………...16
第三章 三維剛性車橋互制元素理論………………………..19
3.1 前言………………….…………………....19
3.2 車橋互制理論模式………….…………....20
3.3 Newmark-β法..………….…………..…..22
3.4 三維剛性車橋互制理論….………………..23
3.4.1 基本假設……………………………..23
3.4.2 理論推導……………………………..24
3.4.3 建立車體動力平衡方程式…………..26
3.4.4 橋梁動力平衡方程式之建立………..30
3.5 剛性車橋互制方程式…..………...………40
3.6 剛性車橋互制程式分析流程..…..……….41
第四章 衝擊係數…………………………………………....43
4.1 前言…………………………...…………..43
4.2 衝擊係數的定義..……….………………..44
4.3 橋梁中點位移和彎矩的衝擊係數………….45
4.4 扭轉衝擊係數的推導…………….…...….46
4.5 扭轉衝擊係數…………………..……..….49
4.6 高速列車通過所造成的衝擊係數……..….51
4.7 實例分析…………..……………..…….….53
4.8橋梁扭轉共振相消………………..………….54
4.8.1 共振反應...……………………..….55
4.8.2 相消反應…………………..…………57
4.9 結論………………………………………….58
第五章 橋梁和車的互制反應……………………………....59
5.1 前言………………………….………………59
5.2 車橋互制反應分析………………………….59
5.3 2D RVBI 元素和3D RVBI 元素的比較…….59
5.3.1 扭轉效應忽略的適當時機………..…61
5.3.2 2D RVBI 元素和3D RVBI 元素的比
較……………………………...…..…62
5.4 各項參數之效應分析……………..…….…63
5.4.1 車體懸浮質量效應…….…..………63
5.4.2 車體轉動慣量之效應…….……....64
5.4.3 彈簧的勁度效應…………….....…65
5.4.4 車體阻尼效應………..…….....…66
5.4.5 比較不平整度對車體的影響.....…67
5.4.6 錯車效應…………..……….....…68
第六章 結論和展望………………………………………....71
6.1 結論………………………...……..…....71
6.2 展望……..……...……………………....72
參考文獻…………………………....………………………..74

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