結論與建議 - TLCD之高樓抗風設計與應用

本研究針對水平及旋轉運動之變斷面調諧水柱消能系統(Variable Tuned Liquid Column Damper, VTLCD)系統進行動力特性試驗，參考並修正Wu＇s formula 建立水頭損失係數之經驗公式，以供日後 VTLCD 系統究提出之modified Wu’s formula 水頭損失係數經驗公式中考慮了斷面比的影響，可將Wu’s formula 分別針對斷面比 β =1,2 及 3 等

顯著，經驗公式預測值與系統識別結果相當接近；小尺寸VTLCD

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表3.1 變斷面 VTLCD 元件之設計參數(小尺寸，β=0.31)

表3.2 變斷面 VTLCD 元件之設計參數(大尺寸，β=0.31)

表3.3 變斷面 VTLCD 元件之設計參數(小尺寸，β=0.6)

表3.4 變斷面 VTLCD 元件之設計參數(大尺寸，β=1.0)

表3.5 變斷面 VTLCD 元件之設計參數(大尺寸，β=2.0)

表3.6 變斷面 VTLCD 元件之設計參數(大尺寸，β=3.0)

表3.7 各元件之擾動頻率輸入值

80% 171.43 16.01 39.85 16.01 28.02 16.01 25.25 16.01 28.40 16.01

60% 149.06 4.26 28.12 4.26 16.87 4.26 13.89 4.26 17.42 4.26

40% 140.95 1.97 25.64 1.97 14.91 1.97 11.69 1.97 14.91 1.97

20% 157.24 1.10 24.19 1.10 13.47 1.10 10.58 1.10 14.12 1.10

0% ^154.20 ^-- ^24.53 ^-- ^13.47 ^-- ^9.45 ^-- ^14.27

80% 75.52 16.01 28.64 16.01 24.80 16.01 24.22 16.01 28.37 16.01

60% 64.82 4.26 16.82 4.26 11.56 4.26 10.67 4.26 15.23 4.26

40% 56.53 1.97 14.71 1.97 9.63 1.97 8.92 1.97 12.75 1.97

20% 58.78 1.10 13.08 1.10 8.64 1.10 8.04 1.10 11.45 1.10

0% ^62.84 ^-- ^13.69 ^-- ^9.00 ^-- ^7.94 ^-- ^11.35

--表3.8(c) 水平運動 VTLCD 水頭損失係數系統識別結果 (小尺寸 β=0.6)

水頭損失係數δ

頻率比 0.6 0.9 1.0 1.1 1.4

阻塞率 ^識別值 ^預估值 ^識別值 ^預估值 ^識別值 ^預估值 ^識別值 ^預估值 ^識別值 ^預估值

80% 128.91 30.98 53.80 30.98 38.88 30.98 35.39 30.98 41.22 30.98

60% 81.79 8.24 23.40 8.24 14.15 8.24 12.35 8.24 16.40 8.24

80% 69.59 51.64 48.29 51.64 48.55 51.64 43.94 51.64 47.64 51.64

60% 32.77 13.73 13.71 13.73 11.55 13.73 11.51 13.73 12.05 13.73

40% 24.77 6.35 8.15 6.35 5.55 6.35 5.70 6.35 6.73 6.35

80% 136.99 103.28 97.01 103.28 93.75 103.28 94.33 103.28 88.14 103.28

60% 49.89 27.46 27.84 27.46 24.50 27.46 23.80 27.46 22.97 27.46

40% 34.51 12.70 13.89 12.70 11.43 12.70 10.80 12.70 10.79 12.70

20% 24.61 7.08 9.20 7.08 7.38 7.08 7.12 7.08 6.68 7.08

0% ^23.32 ^-- ^8.16 ^-- ^6.24 ^-- ^5.94 ^-- ^5.31

--表3.8(f) 水平運動 VTLCD 水頭損失係數系統識別結果 (大尺寸 β=3.0)

水頭損失係數δ

頻率比 0.6 0.9 1.0 1.1 1.4

阻塞率 ^識別值 ^預估值 ^識別值 ^預估值 ^識別值 ^預估值 ^識別值 ^預估值 ^識別值 ^預估值

80% 196.63 154.92 146.74 154.92 142.36 154.92 140.98 154.92 135.70 154.92

60% 60.12 41.19 34.97 41.19 32.39 41.19 31.76 41.19 30.10 41.19

40% 39.06 19.05 17.12 19.05 14.05 19.05 13.63 19.05 13.58 19.05

20% 33.10 10.62 11.32 10.62 9.33 10.62 8.55 10.62 7.89 10.62

0% ^25.22 ^-- ^9.22 ^-- ^7.65 ^-- ^7.00 ^-- ^5.80 40% 5230 44979 100717 100119 40645 20% 5828 43335 105797 103406 41841 0% 4483 45427 104154 103107 39300

表3.9(c) 小尺寸 VTLCD 系統之雷諾數(β=0.6)

表3.9(f) 大尺寸 VTLCD 系統之雷諾數(β=3.0)

80% 87.69 85.30 84.61 85.30 88.47 85.30 93.25 85.30 116.14 85.30

60% 37.30 19.02 24.93 19.02 24.15 19.02 26.50 19.02 50.29 19.02

40% 31.05 8.56 15.45 8.56 12.51 8.56 15.05 8.56 36.74 8.56

80% 143.10 170.60 149.96 170.60 156.64 170.60 162.94 170.60 197.03 170.60

60% 45.16 38.05 37.88 38.05 38.46 38.05 40.86 38.05 63.82 38.05

40% 28.97 17.11 19.91 17.11 18.80 17.11 20.80 17.11 40.91 17.11

20% 23.51 11.06 14.50 11.06 10.20 11.06 11.54 11.06 33.47 11.06

0% ^22.43 ^-- ^13.38 ^-- ^10.40 ^-- ^11.40 ^-- ^27.58

--表3.10(c) VTLCD 旋轉向於系統識別所得之水頭損失係數 (大尺寸 β=3.0)

水頭損失係數δ

頻率比 0.6 0.9 1.0 1.1 1.4

阻塞率 ^識別值 ^預估值 ^識別值 ^預估值 ^識別值 ^預估值 ^識別值 ^預估值 ^識別值 ^預估值

80% 207.64 255.90 219.87 255.90 218.97 255.90 234.09 255.90 298.52 255.90

60% 54.12 57.07 49.69 57.07 51.07 57.07 56.03 57.07 81.90 57.07

40% 31.71 25.67 24.00 25.67 23.94 25.67 25.87 25.67 43.33 25.67

20% 25.53 16.59 16.49 16.59 15.21 16.59 16.35 16.59 32.65 16.59

0% ^22.18 ^-- ^14.21 ^-- ^12.60 ^-- ^13.46 ^-- ^28.10

表4.1 變斷面 VTLCD 元件之設計參數(實尺寸斷面比β=0.31)

表4.2 御盟建設 20 代建案結構系統參數

表4.5 水之物理性質(SI 制) 5 1000 9.807 1.519E-3 1.519E-6 7.49E-2 8.72E+2 206E+7 1427 10 999.7 9.804 1.307E-3 1.307E-6 7.42E-2 1.23E+3 211E+7 1447

表4.7 孔口板(厚度 1 cm)變形量及應力分析結果

圖1.1 台北國際金融大樓與單擺式 TMD 系統

圖1.2 TLCD 系統於加拿大 Wall center 之減振應用

圖1.3 TLCD 系統於東京 Cosima 旅館之減振應用

圖1.4 TLCD 系統於東京千禧塔之減振應用

圖1.5 TLCD 系統於高塔之減振應用

圖1.6 U 形 TLCD 系統於橋塔之減振應用

圖2.1 等斷面 TLCD 理論推導示意圖

圖2.2 變斷面 VTLCD 理論推導示意圖

橋面板旋轉中心

θ¹ θ² α

圖2.3 旋轉向 VTLCD 理論推導示意圖

圖2.4 單自由度結構裝置變斷面 VTLCD 理論推導示意圖

剖面圖

剖面圖正視圖

單位：

孔口板防水墊蓋板

圖3.3 VTLCD 元件設計詳圖(大尺寸，β= 0.31)

單位：

孔口板 (阻塞率80%) 孔口板 (阻塞率60%)

單位：

孔口板 (阻塞率40%) 孔口板 (阻塞率20%)

圖3.4 孔口板設計詳圖

圖3.5 VTLCD 旋轉運動試驗配置圖波高計

致動器

彈簧

圖3.6 振動台之設計尺寸詳圖

圖3.7 MTS 407 控制器

圖3.8 雷射位移計

圖3.9 波高計(WHA-600 和 WHA-800)

WHA-800

WHA-600

圖3.10(a) 小尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=0.6，β=0.31)

圖3.10(b) 小尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=0.9，β=0.31)

圖3.10(c) 小尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.0，β=0.31)

圖3.10(d) 小尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.1，β=0.31)

圖3.10(e) 小尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.4，β=0.31)

圖3.11(a) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=0.6，β=0.31)

圖3.11(b) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=0.9，β=0.31)

圖3.11(c) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.0，β=0.31)

圖3.11(d) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.1，β=0.31)

圖3.11(e) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.4，β=0.31)

圖3.12(a) 小尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=0.6，β=0.6)

圖3.12(b) 小尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=0.9，β=0.6)

圖3.12(c) 小尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.0，β=0.6)

圖3.12(d) 小尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.1，β=0.6)

圖3.12(e) 小尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.4，β=0.6)

圖3.13(a) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=0.6，β=1.0)

圖3.13(b) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=0.9，β=1.0)

圖3.13(c) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.0，β=1.0)

圖3.13(d) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.1，β=1.0)

圖3.13(e) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.4，β=1.0)

圖3.14(a) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=0.6，β=2.0)

圖3.14(b) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=0.9，β=2.0)

圖3.14(c) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.0，β=2.0)

圖3.14(d) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.1，β=2.0)

圖3.14(e) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.4，β=2.0)

圖3.15(a) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=0.6，β=3.0)

圖3.15(b) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=0.9，β=3.0)

圖3.15(c) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.0，β=3.0)

圖3.15(d) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.1，β=3.0)

圖3.15(e) 大尺寸水平運動 VTLCD 之水柱激盪位移歷時 (頻率比=1.4，β=3.0)