近代橋梁跨度增大，且使用質量較輕之建材，其受風作用之反應亦隨之增加，因此增設減振裝置如調頻液柱阻尼器(Tuned Liquid Column Damper, TLCD)來抑制結構扭轉向振動有其必要性。目前TLCD之應用大多集中於建築物，甚少有橋梁上之應用。因此本文之研究內容將針對結構裝設變斷面TLCD進行基本理論推導，並進行TLCD系統識別以及二自由度系統互制行為之驗證實驗。
考慮單自由度結構裝設變斷面調頻液柱阻尼器進行運動方程式推導，在簡諧外力矩擾動下解出結構與TLCD液面反應之理論解。發現在運動方程式存在一修正項，其為以往文獻所忽略，因此，建構大尺度結構與TLCD模型進行實驗驗證，同時亦進行TLCD自然頻率與水頭損失係數之率定，並藉由驗證實驗結果與理論分析結果間之比較，以釐清該修正項之重要性。
率定結果顯示，三組TLCD自然頻率之率定結果與理論值相當接近，其誤差均於5%之內。水頭損失係數則會隨著孔口板阻塞率ψ與斷面積比ν值變大而變大，並經時間歷時分析驗證。另外，互制驗證實驗顯示，大致上當外力擾動頻率於低頻及共振頻率附近時，考慮修正項時所得到之分析結果較接近實驗結果，因此在運動方程式考慮該修正項是必要的。

Recently, the advancement in construction technology and material has facilitated the construction of lighter bridges with even longer span.  The down side effect that comes with it is the susceptibility of such structures to wind loading.  Thus, the use of vibration control device, such as tuned liquid column damper (TLCD), is becoming more and more necessary.  Since the application of TLCD to civil structures is mostly on buildings, the derivation of the interaction behavior between the TLCD and structure in the torsional motion will have to be addressed.
In this research, a single-degree-of-freedom damped structure equipped with a TLCD in torsional motion is considered to derive the equations of motion.  Consequently, the analytical solution of the structural response and TLCD liquid motion has been derived under the excitation of harmonic loading.  It was found that, in the equations of motion, there exists a modified term which is not considered in the existent literature.  To justify the importance of this term, a large scale structure and TLCD models were constructed and the verification of interaction tests was conducted. Prior to the interaction tests, the properties of the TLCD and structures were also identified respectively and the values obtained were used to compute the analytical solutions from the interaction equations for comparison.
The identification results show that natural frequencies of TLCDs are quite close to the theoretical values with error less than 5%, and the head loss coefficients increase with the increase of the blocking ratio and cross-section ratio. On the other hand, the interaction tests show that experimental results are closer to the analytical solution with the modified term considered than without the modified term considered.  Therefore, the incorporation of the modified term in the interaction equations of motion is essential.

目錄	I
表目錄	III
圖目錄	IV
符號對照表	VIII

第一章  緒論	1
1.1 前言	1
1.2 研究動機與目的	2
1.3 文獻回顧	2
1.4 論文架構	9

第二章  理論推導	11
2.1 應用TLCD於結構扭轉向受白噪音擾動情況	11
2.1.1 .扭轉向運動方程式之推導	11
2.1.2 運動方程式之無因次化	18
2.2 應用TLCD於結構扭轉向受簡諧擾動情況	21
2.2.1 運動方程式之推導	21
2.2.2 運動方程式之無因次化	23

第三章  TLCD系統識別之流程與理論	26
3.1 TLCD基本性質之率定	26
3.1.1  TLCD自然頻率率定	27
3.1.2  TLCD水頭損失係數率定	27
3.1.3 利用白噪音強制振動進行水頭損失係數之驗證	30
3.2 結構識別	31
3.2.1 結構頻率與阻尼比之識別	31
3.2.2 結構勁度與質量慣性矩之識別	31

第四章  二自由度系統互制行為─修正項實驗驗證流程與理論	35
4.1 理論推導	35
4.1.1 考慮無修正項情況下之理論推導	35
4.1.2 考慮有修正項情況下之理論推導	39
4.2 修正項實驗驗證流程	43

第五章  實驗架構與設備	45
5.1 模型架構	45
5.1.1 鋼結構模型	45
5.1.2  TLCD元件模型	46
5.1.3 孔口板	46
5.2 量測儀器與設備	46

第六章  實驗結果	54
6.1 結構識別結果	54
6.2 TLCD系統識別結果	54
6.2.1  TLCD自然頻率之率定結果	54
6.2.2 水頭損失係數之率定結果	56
6.2.3 白噪音強制振動之結果	59
6.3 修正項驗證之實驗結果	60

第七章 討論與建議	113

參考文獻	116

 
表目錄

表3.1.1 各組TLCD尺寸規格及參數	33
表3.1.2 水頭損失係數率定之實驗規劃表	33
表5.1.1 鋼結構斷面尺寸	48
表6.1.1 結構頻率與阻尼比	66
表6.1.2 結構扭轉勁度之率定	66
表6.1.3 質量慣性矩之率定	66
表6.2.1  TLCD自然頻率之率定	67
表6.2.2 水頭損失係數之率定	67
表6.2.3 與Wu【25】等人之水頭損失係數比對表	67
表6.3.1  TLCD II (ν=2.0)之力矩大小	68
表6.3.2  TLCD II (ν=2.0)數值分析與實驗扭轉角間之相對誤差	69
表6.3.3  TLCD III (ν=3.0)之力矩大小	70
表6.3.4  TLCD III (ν=3.0)數值分析與實驗扭轉角間之相對誤差	71
表6.3.5  TLCD II (ν=2.0)數值分析與實驗液面振幅間之相對誤差	72
表6.3.6  TLCD III (ν=3.0)數值分析與實驗液面振幅間之相對誤差	73


 
圖目錄

圖2.1.1 扭轉向TLCD理論推導示意圖	25
圖3.1.1  TLCD模型示意圖	34
圖3.1.2 結構系統識別之實驗架構	34
圖5.1.1 實驗架構示意圖	49
圖5.1.2 實驗模型架構	49
圖5.1.3  TLCD實驗模型(ν=3.0)	50
圖5.1.4 孔口板	50
圖5.1.5  MTS 407控制器	51
圖5.1.6 資料擷取系統	51
圖5.1.7  1.5 ton致動器	52
圖5.1.8  1.5 ton致動器與力規(Loadcell)	52
圖5.1.9 雷射位移計	53
圖5.1.10 波高計	53
圖6.1.1  TLCD II (ν=2.0)自由振動歷時圖	74
圖6.1.2  TLCD III (ν=3.0)自由振動歷時圖	74
圖6.1.3  TLCD II (ν=2.0)扭轉勁度率定	75
圖6.1.4  TLCD III (ν=3.0)扭轉勁度率定	75
圖6.2.1  TLCD I (ν=1.0)自由振動位移歷時圖	76
圖6.2.2  TLCD II (ν=2.0)自由振動位移歷時圖	76
圖6.2.3  TLCD III (ν=3.0)自由振動位移歷時圖	76
圖6.2.4  TLCD I (ν=1.0)外力擾動頻率比與液面振幅之關係圖	77
圖6.2.5  TLCD II (ν=2.0)外力擾動頻率比與液面振幅之關係圖	77
圖6.2.6  TLCD III (ν=3.0)外力擾動頻率比與液面振幅之關係圖	78
圖6.2.7  TLCD I (ν=1.0)於簡諧外力擾動下之液面振幅歷時圖
(a) ψ = 0%	79
(b) ψ = 20%	79
(c) ψ = 40%	79
(d) ψ = 60%	80
(e) ψ = 80%	80
圖6.2.8  TLCD II (ν=2.0)於簡諧外力擾動下之液面振幅歷時圖
(a) ψ = 0%	81
(b) ψ = 20%	81
(c) ψ = 40%	81
(d) ψ = 60%	82
(e) ψ = 80%	82
圖6.2.9  TLCD III (ν=3.0)於簡諧外力擾動下之液面振幅歷時圖
(a) ψ = 0%	83
(b) ψ = 20%	83
(c) ψ = 40%	83
(d) ψ = 60%	84
(e) ψ = 80%	84
圖6.2.10 孔口板阻塞率與水頭損失係數之關係圖	85
圖6.2.11 TLCD I (ν=1.0)於白噪音強制振動下之液面振幅歷時圖
(a) ψ = 0%	86
(b) ψ = 40%	86
(c) ψ = 80%	86
圖6.2.12 TLCD II (ν=2.0)於白噪音強制振動下之液面振幅歷時圖
(a) ψ = 0%	87
(b) ψ = 40%	87
(c) ψ = 80%	87
圖6.2.13 TLCD III (ν=3.0)於白噪音強制振動下之液面振幅歷時圖
(a) ψ = 0%	88
(b) ψ = 40%	88
(c) ψ = 80%	88
圖6.3.1 考慮修正項與否時扭轉角與外力頻率比之關係圖(ν=2.0, ψ=0%)	89
圖6.3.2 考慮修正項與否時扭轉角與外力頻率比之關係圖(ν=2.0, ψ=20%)	89
圖6.3.3 考慮修正項與否時扭轉角與外力頻率比之關係圖(ν=2.0, ψ=40%)	90
圖6.3.4 考慮修正項與否時扭轉角與外力頻率比之關係圖(ν=2.0, ψ=60%)	90
圖6.3.5 考慮修正項與否時扭轉角與外力頻率比之關係圖(ν=2.0, ψ=80%)	91
圖6.3.6 考慮修正項與否時扭轉角之誤差比較(ν=2.0, ψ=0%)	91
圖6.3.7 考慮修正項與否時扭轉角之誤差比較(ν=2.0, ψ=20%)	92
圖6.3.8 考慮修正項與否時扭轉角之誤差比較(ν=2.0, ψ=40%)	92
圖6.3.9 考慮修正項與否時扭轉角之誤差比較(ν=2.0, ψ=60%)	93
圖6.3.10 考慮修正項與否時扭轉角之誤差比較(ν=2.0, ψ=80%)	93
圖6.3.11 考慮修正項與否時扭轉角與外力頻率比之關係圖(ν=3.0, ψ=0%)	94
圖6.3.12 考慮修正項與否時扭轉角與外力頻率比之關係圖(ν=3.0, ψ=20%)	94
圖6.3.13 考慮修正項與否時扭轉角與外力頻率比之關係圖(ν=3.0, ψ=40%)	95
圖6.3.14 考慮修正項與否時扭轉角與外力頻率比之關係圖(ν=3.0, ψ=60%)	95
圖6.3.15 考慮修正項與否時扭轉角與外力頻率比之關係圖(ν=3.0, ψ=80%)	96
圖6.3.16 考慮修正項與否時扭轉角之誤差比較(ν=3.0, ψ=0%)	96
圖6.3.17 考慮修正項與否時扭轉角之誤差比較(ν=3.0, ψ=20%)	97
圖6.3.18 考慮修正項與否時扭轉角之誤差比較(ν=3.0, ψ=40%)	97
圖6.3.19 考慮修正項與否時扭轉角之誤差比較(ν=3.0, ψ=60%)	98
圖6.3.20 考慮修正項與否時扭轉角之誤差比較(ν=3.0, ψ=80%)	98
圖6.3.21 考慮修正項與否時液面振幅與外力頻率比之關係圖(ν=2.0, ψ=0%)	99
圖6.3.22 考慮修正項與否時液面振幅與外力頻率比之關係圖(ν=2.0, ψ=20%)	99
圖6.3.23 考慮修正項與否時液面振幅與外力頻率比之關係圖(ν=2.0, ψ=40%)	100
圖6.3.24 考慮修正項與否時液面振幅與外力頻率比之關係圖(ν=2.0, ψ=60%)	100
圖6.3.25 考慮修正項與否時液面振幅與外力頻率比之關係圖(ν=2.0, ψ=80%)	101
圖6.3.26 考慮修正項與否時液面振幅之誤差比較(ν=2.0, ψ=0%)	101
圖6.3.27 考慮修正項與否時液面振幅之誤差比較(ν=2.0, ψ=20%)	102
圖6.3.28 考慮修正項與否時液面振幅之誤差比較(ν=2.0, ψ=40%)	102
圖6.3.29 考慮修正項與否時液面振幅之誤差比較(ν=2.0, ψ=60%)	103
圖6.3.30 考慮修正項與否時液面振幅之誤差比較(ν=2.0, ψ=80%)	103
圖6.3.31 考慮修正項與否時液面振幅與外力頻率比之關係圖(ν=3.0, ψ=0%)	104
圖6.3.32 考慮修正項與否時液面振幅與外力頻率比之關係圖(ν=3.0, ψ=20%)	104
圖6.3.33 考慮修正項與否時液面振幅與外力頻率比之關係圖(ν=3.0, ψ=40%)	105
圖6.3.34 考慮修正項與否時液面振幅與外力頻率比之關係圖(ν=3.0, ψ=60%)	105
圖6.3.35 考慮修正項與否時液面振幅與外力頻率比之關係圖(ν=3.0, ψ=80%)	106
圖6.3.36 考慮修正項與否時液面振幅之誤差比較(ν=3.0, ψ=0%)	106
圖6.3.37 考慮修正項與否時液面振幅之誤差比較(ν=3.0, ψ=20%)	107
圖6.3.38 考慮修正項與否時液面振幅之誤差比較(ν=3.0, ψ=40%)	107
圖6.3.39 考慮修正項與否時液面振幅之誤差比較(ν=3.0, ψ=60%)	108
圖6.3.40 考慮修正項與否時液面振幅之誤差比較(ν=3.0, ψ=80%)	108
圖6.3.41 TLCD II (ν=2.0)於白噪音強制振動下之二自由度歷時圖
(a) ψ=0%之轉角歷時曲線	109
(b) ψ=0%之液面振幅歷時曲線	109
(c) ψ=40%之轉角歷時曲線	109
(d) ψ=40%之液面振幅歷時曲線	110
(e) ψ=80%之轉角歷時曲線	110
(f) ψ=80%之液面振幅歷時曲線	110
圖6.3.42 TLCD III (ν=3.0)於白噪音強制振動下之二自由度歷時圖
(a) ψ=0%之轉角歷時曲線	111
(b) ψ=0%之液面振幅歷時曲線	111
(c) ψ=40%之轉角歷時曲線	111
(d) ψ=40%之液面振幅歷時曲線	112
(e) ψ=80%之轉角歷時曲線	112
(f) ψ=80%之液面振幅歷時曲線	112

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