結論

本計劃全程三年，規劃之研究項目包括靜力載重試驗及衝擊載重(階梯式驟加 外力)試驗等。本研究完成：應力波傳之理論分析程式(靜力與動力分析)、三維鋁 模型剛架之製作、波動量測儀器之採購、靜力試驗及衝擊載重試驗(含空心與實心 構材斷面)。根據理論分析與試驗的結果，吾人歸納以下結論:

(1) 迴傳矩陣法(Reverberation Matrix Method, RMM)分析所得之結果與有限元素軟 體 SAP2000 分析所得之結果相當一致；兩層樓三維鋁模型剛架之靜力試驗結果 顯示，試驗與理論分析結果契合的程度相當高，印證以迴傳矩陣法分析靜力結 構之精確性。

(2) 利用釣魚線懸吊質塊，並以噴燈迅速將釣魚線燒斷之驟加衝擊力機構相當穩 定，每次試驗所產生之衝擊力約略相等，有助於重複進行相同的試驗。此外，

觸發訊號的設計可在衝擊力施加於結構的瞬間即開始擷取資料。

(3) 空心斷面之兩層樓三維鋁模型構架之驟加衝擊載重試驗顯示，試驗結果與理論 分析結果二者的趨勢極為相符，大趨勢可充分掌握，惟理論分析的結果較為平 滑，試驗的結果則有較多高頻的波動反應。

(4) 實心斷面之兩層樓三維鋁模型構架之驟加衝擊載重試驗顯示，試驗結果與理論 分析結果二者的趨勢極為相符，試驗應變值與理論分析的結果於 50 個正規化 時間內契合的程度相當高。此外，應變訊號抖動的情形已顯少發生，說明鋁構 架模型採用空心斷面或是實心斷面製作，其應力波動的特性將有所差異，空心 斷面之高頻波動之特性須另外建立理論分析模型加以考慮。

參考文獻

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表 6.1 鋁材之材料性質(空心斷面)

物 理 量 大 小

楊氏模數 70

GPa

剪力模數 26

GPa

密 度 2700

kg m³

斷面尺寸 2 . 5

cm

× 2 . 5

cm

× 0 . 2

cm

斷 面 積 1.840 cm

²

慣 性 矩 1.635 cm

⁴

極慣性矩 3.270 cm

²

剪力係數 κ π

²

12

卜桑比 ν 0.348

表 6.2 鋁材之材料性質(實心斷面)

物 理 量 大 小

楊氏模數 70 GPa

剪力模數 26 GPa

密 度 2700

kg m³

斷面尺寸 1 . 9

cm

× 1 . 9

cm

斷 面 積 3.61

cm²

慣 性 矩 1.086 cm

⁴

極慣性矩 2.172 cm

²

剪力係數 κ π

²

12

卜桑比 ν 0.348

Spectrum Relations f or the Timoshenko Beam Theory

Frequency (rad) Speeds:c/c0 ,cg/c0

0 100 200 300

0 0.1 0.2 0.3

圖 2.3 白努利樑的撓曲波波速與頻率的關係

0 ⁵⁰⁰⁰ 10000 ¹⁵⁰⁰⁰ 20000 ²⁵⁰⁰⁰ 30000

0 100 200 300 400

50 150 250 350

-50

real part of k3 image part of k3 real part of k4 image part of k4

Frequency (rad/sec)

Wavenumber

Spectrum Relations for the Timoshenko Beam theory without Damping

圖 2.4 提摩盛科樑的撓曲波波數與頻率的關係(無阻尼)

0 200000 400000 600000 800000 1000000 0

0.5 1 1.5 2 2.5

Bernoulli beam(phase speed) Timoshenko Beam(phase speeds[Mode1]) Timoshenko Beam(phase speeds[Mode2]) Timoshenko Beam(group speeds[Mode1]) Timoshenko Beam(group speeds[Mode2]) Bernoulli beam(group speed)

Spectrum Relations f or the Timoshenko Beam Theory

Frequency (Hz) Speeds:c/c_{0 ,}c_g/c₀

圖 2.5 提摩盛科樑的撓曲波波速與頻率的關係

0 ⁵⁰⁰⁰ 10000 ¹⁵⁰⁰⁰ 20000 ²⁵⁰⁰⁰ 30000

0 100 200 300 400

50 150 250 350

-50

real part of k3 image part of k3 real part of k4 image part of k4

Frequency (rad/sec)

Wavenumber

Spectrum Relations for the Timoshenko Beam theory with Damping

圖 2.6 提摩盛科樑的撓曲波波速與頻率的關係(有阻尼)

)]

( 1 [ )

(t W H t F =− −

圖 2.7 三維剛架結構

J

zKJ

xJK

xKJ

X K

Y

Z zJK

zJK KJ

y

圖 2.8 桿件的座標系統

0 ¹⁰ 20 ³⁰ 40 ⁵⁰ 60 ⁷⁰ 80 ⁹⁰ -1

0 1 2 3

-0.5 0.5 1.5 2.5

Solution A Solution B

Normalized Displacement

Normalized Time

×10^-4

圖 4.2 節點 1 的垂直位移。 解

a_A

;

a_B

0 ¹⁰ 20 ³⁰ 40 ⁵⁰ 60 ⁷⁰ 80 ⁹⁰

-0.6 -0.4 -0.2 0 0.2 0.4

-0.5 -0.3 -0.1 0.1 0.3

Solution A Solution B

Normalized Displacement

Normalized Time

圖 4.3 節點 6 的垂直位移。

解a_A

；

a_B

照片 6.1(a) 鋁模型剛架

照片 6.1(b) 鋁模型剛架(短向)

照片 6.1(c) 鋁模型剛架(長向)

圖 6.1(a) 鋁模型剛架(上視圖)

圖 6.1(b) 鋁模型剛架-側視圖(短向)

圖 6.1(c) 鋁模型剛架-側視圖(長向)

掛勾 滑輪

釣魚線

滑輪支撐柱

質塊

照片 6.2(a) 加載機構

掛勾

釣魚線

觸發訊號源(Trigger Source) 壓電式應變計

照片 6.2(b) 釣魚線固定於掛勾

滑輪

釣魚線 掛勾

釣魚線

照片 6.2(c) 釣魚線跨過滑輪

釣魚線

質塊

照片 6.2(d) 釣魚線懸吊質塊

照片 6.2(e) 質塊

照片 6.3 噴燈及釣魚線

應變計

照片 6.4(a) 黏貼於鋁構架模型之應變計

應變計

應變計接線

照片 6.4(b) 黏貼於鋁構架模型之應變計

照片 6.5 衝擊載重試驗之儀器設備

外部觸發通道

照片 6.6(a) 高頻示波器(前視)

RS232 接附

照片 6.6(b) 高頻示波器(後視)

照片 6.7(a) 訊號調節放大器-惠斯敦電橋(前視)

軍用接頭

應變計接線

照片 6.7(b) 訊號調節放大器-惠斯敦電橋(後視)

壓電式應變計 軍用接頭 8mm 3.2mm 1.6mm

電阻式應變計

照片 6.8 應變計及軍用接頭

0 20 40 60 80 100 120 140 160 180 20 Normalized Time

0 -200

-150 -100 -50 0 50 100 150 200

Strain(µ)

Beam 3-6 (Right) Axial Wave + Bending Wave

Theoretical Experimental

圖 6.2 軸向波與彎矩波產生之應變(梁桿件 3-6-Right)

0 20 40 60 80 100 120 140 160 180 20

Normalized Time

0 -200

-150 -100 -50 0 50 100 150 200

Strain(µ)

Beam 3-6 (Left) Axial Wave + Bending Wave

Theoretical Experimental

圖 6.3 軸向波與彎矩波產生之應變(梁桿件 3-6-Left)

0 20 40 60 80 100 120 140 160 180 20 Normalized Time

0 -100

-50 0 50 100

Strain(µ)

Beam 5-11 (Front) Axial Wave + Bending Wave

Theoretical Experimental

圖 6.4 軸向波與彎矩波產生之應變(梁桿件 5-11-Front)

0 20 40 60 80 100 120 140 160 180 20

Normalized Time

0 -100

-50 0 50 100

Strain(µ)

Beam 5-11 (Bottom) Axial Wave + Bending Wave

Theoretical Experimental

圖 6.5 軸向波與彎矩波產生之應變(梁桿件 5-11-Bottom)

0 20 40 60 80 100 120 140 160 180 20 Normalized Time

0 -200

-150 -100 -50 0 50 100 150 200

Strain(µ)

Beam 8-11 (Top) Axial Wave + Bending Wave

Theoretical Experimental

圖 6.6 軸向波與彎矩波產生之應變(梁桿件 8-11-Top)

0 20 40 60 80 100 120 140 160 180 20

Normalized Time

0 -200

-150 -100 -50 0 50 100 150 200

Strain(µ)

Beam 8-11 (Bottom) Axial Wave + Bending Wave

Theoretical Experimental

圖 6.7 軸向波與彎矩波產生之應變(梁桿件 8-11-Bottom)

0 20 40 60 80 100 120 140 160 180 200 Normalized Time

-50 -25 0 25 50

Strain(µ)

Column 4-5 (Front) Axial Wave + Bending Wave

Theoretical Experimental

圖 6.8 軸向波與彎矩波產生之應變(柱桿件 4-5-Front)

0 20 40 60 80 100 120 140 160 180 200

Normalized Time -50

-25 0 25 50

Strain(µ)

Column 4-5 (Back) Axial Wave + Bending Wave

Theoretical Experimental

圖 6.9 軸向波與彎矩波產生之應變(柱桿件 4-5-Back)

0 20 40 60 80 100 120 140 160 180 20 Normalized Time

0 -100

0 100 200

Strain(µ)

Column 8-9 (Front) Axial Wave + Bending Wave

Theoretical Experimental

圖 6.10 軸向波與彎矩波產生之應變(柱桿件 8-9-Front)

0 20 40 60 80 100 120 140 160 180 20

Normalized Time

0 -250

-200 -150 -100 -50 0 50 100 150 200

Strain(µ)

Column 8-9 (Back) Axial Wave + Bending Wave

Theoretical Experimental

圖 6.11 軸向波與彎矩波產生之應變(柱桿件 8-9-Back)

-0.002 -0.001 0.000 0.001 0.002 0.003 0.004 Time (sec)

-0.5 0.0 0.5 1.0 1.5 2.0

Triger Source(V)

-0.002 -0.001 0.000 0.001 0.002 0.003 0.004 Time (sec)

-0.05 0.00 0.05 0.10

Strain (V)

圖 6.12 觸發訊號源之製作

-0.001 0.000 0.001 0.002 0.003 0.004

Time (sec) -0.60

-0.30 0.00 0.30 0.60

Triger Source (V)

F = 8 k g F = 1 6 k g

V = 0 . 0 5 Trigger

Point

圖 6.13 壓電式應變計觸發訊號源之歷時

0 20 40 60 80 100 120 140 160 180 200 Normalized Time

-150 -100 -50 0 50 100 150

Strain(µ)

Column 8-9 (Front)

Theoretical Experimental

圖 6.14(a) 軸向波與彎矩波產生之應變(柱桿件 8-9-Front)

0 20 40 60 80 100 120 140 160 180 200

Normalized Time -150

-100 -50 0 50 100 150

Strain(µ)

Column 8-9 (Back)

Theoretical Experimental

圖 6.14(b) 軸向波與彎矩波產生之應變(柱桿件 8-9-Back)

0 20 40 60 80 100 120 140 160 180 200

Normalized Time

-75 -50 -25 0 25 50 75

Strain(µ)

Column 7-8 (Front)

Theoretical Experimental

圖 6.15 (a) 軸向波與彎矩波產生之應變(柱桿件 7-8-Front)

0 20 40 60 80 100 120 140 160 180 200

Normalized Time

-75 -50 -25 0 25 50 75

Strain(µ)

Column 7-8 (Back)

Theoretical Experimental

圖 6.15 (b) 軸向波與彎矩波產生之應變(柱桿件 7-8-Back)

0 20 40 60 80 100 120 140 160 180 200 Normalized Time

-100 -50 0 50 100

Strain(µ)

Beam 8-11 (Top)

Theoretical Experimental

圖 6.16 (a) 軸向波與彎矩波產生之應變(梁桿件 8-11-Top)

0 20 40 60 80 100 120 140 160 180 200

Normalized Time -100

-50 0 50 100

Strain(µ)

Beam 8-11 (Bottom)

Theoretical Experimental

圖 6.16 (b) 軸向波與彎矩波產生之應變(梁桿件 8-11-Bottom)

0 20 40 60 80 100 120 140 160 180 200 Normalized Time

-50 -25 0 25 50

Strain(µ)

Column 4-5 (Front)

Theoretical Experimental

圖 6.17(a) 軸向波與彎矩波產生之應變(柱桿件 4-5-Front)

0 20 40 60 80 100 120 140 160 180 200 Normalized Time

-50 -25 0 25 50

Strain(µ)

Column 4-5 (Back)

Theoretical Experimental

圖 6.17(b) 軸向波與彎矩波產生之應變(柱桿件 4-5-Back)

在文檔中 三維剛架結構之迴傳波射動力分析與模型實驗(3/3) (頁 56-86)