臺灣博碩士論文加值系統

奈米碳管具有優良的機械與化學特性，因此科學家們紛紛以奈米碳管為補強材來製作高性能的奈米複合材料。本文將以多壁奈米碳管補強高分子樹脂材料，探討此高分子複合材料於動態特性上的表現，其動態特性包含自然頻率與耗損因子。受動態負載之結構中所選用的材料直接影響機具結構的動態特性，加有奈米碳管的高分子樹脂，可提升材料的剛性，提升結構的共振頻率，減少因共振現象對結構的影響；而奈米碳管與高分子基材間良好的界面特性，可提升材料的阻尼特性。
本研究將以有限元素分析模擬結構的振動模態與自然頻率，並與振動實驗量測結果比較。實驗結果所獲得的振動頻譜響應曲線可利用半能量頻寬法計算材料之耗損因子。最後將高分子複合材料運用於三明治結構中核心部份，表面材料則選用碳纖維疊層板，探討不同纖維疊層角對三明治結構態特性的影響。由於有限單元分析需材料常數，因而也將材料進行拉伸實驗，由實驗結果探討奈米複材機械特性，最後以SEM觀察材料破壞表面，了解材料受拉伸負載的破壞機制與碳管於樹脂中的分佈情形。

The carbon nanotubes (CNTs) have better mechanical and chemical properties. Researchers used CNTs as reinforcement to fabricate nano- composites. In this study, multi-walled nanotubes (MWNTs) were used to reinforce the polymer resin, and the dynamic properties of the nanocomposites were investigated experimentally. Dynamic properties such as natural frequency and loss factor were measured. When the structure was subjected to dynamic loading, the material used would influence the dynamic characteristics of the structure directly. The addition of MWNTs in the polymer matrix increased the stiffness and natural frequency of the structure, and decreased the effect of resonance. There is good interfacial characteristic between the MWNTs and polymer resin which increased the damping characteristic.
In this study, finite element analysis was used to simulate the structural mode shape and natural frequency, and the results were compared to the results obtained from the vibration test. Moreover, Half-Power Bandwidth method was used to calculate the loss factor from the frequency spectrum response. At last, polymeric composites were applied to the core part of the sandwich structure, and graphite/epoxy laminates were applied to be surface material. The effects of different ply-angle on the dynamic characteristics of graphite/epoxy laminates were investigated. Material parameters should be defined in the analysis. The specimen was subjected to tension test. With the test, the mechanical properties of nanocomposites were discussed. Finally, SEM was used to observe the fractured surface of nanocomposites to understand the failure mechanism of the material subject to tension loading and the distribution of the MWNTs in the resin matrix.

目錄
頁次
摘要………………………………………………………………………i
誌謝……………………………………………………………………...iii
目錄……………………………………………………………………...iv
圖表目錄………………………………………………………………..vii
第一章 簡介 1
1.1 研究動機 1
1.2 文獻回顧 1
1.3研究目標 6
第二章 結構動態行為分析 8
2.1 複材疊層板有限單元分析 8
2.2 模態分析 11
2.3 理想三明治結構模型 12
2.4阻尼的種類 13
2.4.1黏滯阻尼 13
2.4.2庫倫阻尼 13
2.4.3結構阻尼 14
2.5阻尼量測 15
2.5.1半功率頻寬法 15
2.5.2自然衰減法 17
2.6層狀懸臂樑結構振動理論 18
2.6.1均勻樑結構 19
2.6.2單邊阻尼之樑結構 19
2.6.3雙邊阻尼之樑結構 20
2.6.4三明治樑結構 20
第三章 實驗設備與程序 22
3.1 實驗設備 22
3.1.1 製作複材疊層板之實驗設備 22
3.1.2 高分子複材之實驗設備 22
3.1.3 量測材料常數之實驗設備 23
3.1.4 材料密度量測所需之實驗設備 23
3.1.5 動態特性量測所需之實驗設備 23
3.1.6三明治結構破壞機制所需之實驗設備 24
3.2 複材疊層板試片製作 24
3.3高分子複合材料試片製作 25
3.3.1 多壁碳管/環氧樹脂複合材料 25
3.3.2 多壁碳管/酚醛樹脂複合材料 27
3.4 三明治結構試片製作 28
3.5 材料常數量測 29
3.5.1 軸向楊氏係數( )和蒲松比( ) 30
3.5.2 橫向楊氏係數( ) 30
3.5.3 剪力模數( ) 30
3.5.4 高分子複材之楊氏係數( )與蒲松比( ) 31
3.5.5 拉伸實驗數據統計 31
3.6動態特性實驗 32
3.6.1 自由振動系統實驗 32
3.6.2 強制振動系統實驗 33
第四章 結果與討論 35
4.1拉伸試驗結果 35
4.1.1多壁碳管/環氧樹脂複合材料拉伸試驗結果 35
4.1.2多壁碳管/酚醛樹脂複合材料拉伸試驗結果 36
4.2動態特性實驗結果 36
4.2.1多壁碳管/環氧樹脂複合材料動態實驗結果 37
4.2.2多壁碳管/酚醛樹脂複合材料動態實驗結果 38
4.2.3碳纖維疊層板動態實驗結果 39
4.3 三明治結構不同參數探討 40
4.3.1 不同核心厚度三明治結構動態實驗結果 40
4.3.2不同碳纖維疊層角度表面材料之三明治結構動態實驗結果 40
4.3.3不同核心材料之三明治結構動態實驗結果 41
4.3.4三明治結構三點彎矩實驗結果 41
4.4 ANSYS模態分析 42
4.4.1高分子奈米複材模態分析 43
4.4.2碳纖維疊層板模態分析 43
4.4.3三明治結構模態分析 44
4.5破壞面SEM觀察 44
第五章 結論 46
參考文獻 47
圖表目錄 52





圖 表 目 錄
表2.1 第N個模態之係數( ) 52
表3.1 標準偏差比 （用於實驗數據處理） 52
表4.1 多壁碳管/環氧樹脂拉伸試驗結果(括弧內為標準差) 53
表4.2 多壁碳管/酚醛樹脂拉伸試驗結果(括弧內為標準差) 53
表4.3 不同輸出訊號所得純環氧樹脂強制振動實驗結果 54
表4.4 多壁碳管/環氧樹脂複材樑強制振動自然頻率(H )實驗結果 54
表4.5 多壁碳管/環氧樹脂複材樑自然振動自然頻率(H )實驗結果 55
表4.6 多壁碳管/環氧樹脂複材樑強制振動耗損因子實驗結果 55
表4.7 多壁碳管/環氧樹脂複材樑自然振動耗損因子實驗結果 56
表4.8 多壁碳管/酚醛樹脂複材樑自然頻率(H )實驗結果 56
表4.9 無後處理多壁碳管/酚醛樹脂複材樑耗損因子實驗結果 57
表4.10 經後處理多壁碳管/酚醛樹脂複材樑耗損因子實驗結果 57
表4.11 碳纖維複材疊層板自然頻率(H )實驗結果 58
表4.12 碳纖維複材疊層板耗損因子實驗結果 58
表4.13 不同核心厚度三明治結構動態實驗結果(表面材：[0]4碳纖維疊層板，核心材：環氧樹脂) 59
表4.14 以不同結構型式環氧樹脂懸臂樑耗損因子量測結果比較 59
表4.15 不同碳纖維疊層角度表面材料之三明治結構動態實驗結果(核心材：環氧樹脂) 60
表4.16 不同核心材料之三明治結構動態實驗結果(表面材：[0]4碳纖維疊層板) 61
表4.17 三明治結構三點彎矩實驗結果(表面材：[0]4碳纖維疊層板，核心材：環氧樹脂) 61
表4.18 多壁碳管/環氧樹脂自然頻率(H )分析與實驗值比較 62
表4.19 多壁碳管/酚醛樹脂自然頻率(H )分析與實驗值比較 63
表4.20 碳纖維疊層板自然頻率(H )分析與實驗值比較 64
表4.21 三明治結構自然頻率(H )分析與實驗值比較 65
圖2.1 S 99單元示意圖 66
圖2.2 理想三明治結構示意圖 66
圖2.3 S 46單元示意圖 67
圖2.4 S 45單元示意圖 67
圖2.5 流體間之黏滯效果示意圖 68
圖2.6 庫倫阻尼示意圖 68
圖2.7 庫倫阻尼振動響應圖 69
圖2.8 單一自由度之結構阻尼系統 69
圖2.9 半功率頻寬法示意圖 70
圖2.10 自然衰減法示意圖 70
圖2.11 不同種類之懸臂樑結構 71
圖3.1 熱壓機 71
圖3.2 空壓機 72
圖3.3 真空幫浦 72
圖3.4 鑽石切割機 73
圖3.5 真空烘箱 73
圖3.6 磁力攪拌器 74
圖3.7 超音波振動儀 74
圖3.8 小型鑽石切割機 75
圖3.9 拉壓試驗機 75
圖3.10 拉壓試驗機 76
圖3.11 材料密度量測設備 76
圖3.12 自然振動量測之動態分析儀 77
圖3.13 強制振動量測之控制電腦 77
圖3.14 激振器 78
圖3.15 雷射速度計 78
圖3.16 三點彎矩儀器 79
圖3.17 三點彎矩實驗夾頭示意圖 79
圖3.18 製作纖維複材疊層板之輔助材料堆疊示意圖 80
圖3.19 製作纖維複材疊層板之上、下模具 80
圖3.20 製作纖維複材疊層板之溫度與壓力控制圖 81
圖3.21 多壁碳管裸體SEM 圖 81
圖3.22 製作多壁碳管/環氧樹脂複合材料之上下模、脫模布及鋁框擺設示意圖 82
圖3.23 高分子試片成型模具 82
圖3.24 製作多壁碳管/酚醛樹脂複合材料之上下模、脫模布及鋁框擺設示意圖 83
圖3.25 三明治試片尺寸示意圖 83
圖3.26 纖維複材疊層板材料常數量測所使用試片尺寸 84
圖3.27 軸向應力與軸向應變應力－應變關係圖 84
圖3.28 橫向應變與軸向應變關係圖 85
圖3.29 橫向應力與橫向應變繪成應力－應變關係圖 85
圖3.30 平面剪應力－平面剪應變關係圖 86
圖3.31 高分子複材拉伸試片尺寸示意圖 86
圖3.32 自由振動系統實驗示意圖 87
圖3.33 振動實驗試片與夾頭尺寸示意圖 87
圖3.34 強制振動系統實驗示意圖 88
圖4.1 多壁碳管/環氧樹脂不同碳管含量與楊氏係數關係圖 88
圖4.2 多壁碳管/環氧樹脂不同碳管含量與抗拉強度關係圖 89
圖4.3 多壁碳管/環氧樹脂不同碳管含量應力－應變關係圖 89
圖4.4 多壁碳管/酚醛樹脂不同碳管含量與楊氏係數關係圖 90
圖4.5 多壁碳管/酚醛樹脂於不同碳管含量與抗拉強度關係圖 90
圖4.6 環氧樹脂懸臂樑不同輸出訊號頻譜響應曲線圖 91
圖4.7 環氧樹脂懸臂樑不同雷射點對焦位置示意圖 92
圖4.8 環氧樹脂懸臂樑不同雷射對焦位置頻譜響應曲線圖 93
圖4.9 環氧樹脂懸臂樑強制振動頻譜響應曲線圖 94
圖4.10 環氧樹脂懸臂樑自由振動頻譜響應曲線圖 94
圖4.11 多壁碳管/環氧樹脂不同碳管含量強制振動實驗結果 95
圖4.12 多壁碳管/酚醛樹脂不同碳管含量振動實驗結果 96
圖4.13 環氧樹脂與酚醛樹脂耗損因子關係圖 97
圖4.14 不同纖維疊層角度於不同模態時振動實驗結果 98
圖4.15 不同核心厚度三明治結構(表面材：[0]4碳纖維疊層板，核心材：環氧樹脂)於不同模態時動態實驗結果 99
圖4.16 表面材料為不同纖維疊層角度三明治結構(核心材：環氧樹脂)於不同模態時動態實驗結果 100
圖4.17 不同核心材料三明治結構(表面材：[0]4碳纖維疊層板)於不同模態時耗損因子動態實驗結果 101
圖4.18 不同表面材料之三明治結構彎曲力矩與撓度關係圖 102
圖4.19 核心材料為環氧樹脂之三明治結構(表面材：[0]4碳纖維疊層板)受三點彎矩破壞圖 102
圖4.20 核心材料為酚醛樹脂之三明治結構(表面材：[0]4碳纖維疊層板)受三點彎矩破壞照相圖 103
圖4.21 高分子複材模態分析網格細分圖 103
圖4.22 高分子複材樑模態分析結果與實驗值比較圖 104
圖4.23 高分子複材前八個模態振型圖 105
圖4.24 碳纖維疊層板模態分析網格細分圖 106
圖4.25 碳纖維疊層板模態分析結果與實驗值比較圖 106
圖4.26 碳纖維疊層板前八個模態振型圖 107
圖4.27 三明治結構模態分析網格細分圖 108
圖4.28 三明治結構模態分析結果與實驗值比較圖 108
圖4.29 三明治結構前八個模態振型圖 109
圖4.30 純環氧樹脂破壞面SEM圖 110
圖4.31 5WT%多壁碳管/環氧樹脂試片破壞面SEM圖 111
圖4.32 5WT% 多壁碳管/酚醛樹脂試片破壞面SEM圖 113

1. S. Iijima, “Helical Microtubules of Graphitic Carbon,” Nature, Vol. 354, pp. 56-58, 1991.
2. E. T. Thostenson, Z. Ren and T. W. Chou, “Advances in the Science and Technology of Carbon Nanotubes and their Composites : a review,” Composites Science and Technology, Vol. 61, pp. 1899-1912, 2001.
3. S. Xie, W. Li, Z. Pan, B. Chang and L. Sun, “Mechanical and Physical Properties on Carbon nanotube,” Journal of Physics and Chemistry of Solids, Vol. 61, pp. 1153-1158, 2000.
4. B. G. Demczyk, Y. M. Wang, J. Cumings, M. Hetman, W. Han, A. Zettl and R. O. Ritchie, “Direct Mechanical Measurement of the Tensile Strength and Elastic Modulus of Multiwalled Carbon Nanotubes,” Materials Science and Engineering A, Vol. 334, pp. 173-178, 2002.
5. A. Allaoui, S. Bai, H. M. Cheng and J.B. Bai, “Mechanical and Electrical Properties of a MWNT/Epoxy Composite,” Composites Science and Technology, Vol. 62, pp. 1993–1998, 2002.
6. J. B. Bai, “Evidence of the Reinforcement Role of Chemical Vapour Deposition Multi-Walled Carbon Nanotubes in a Polymer Matrix,” Letters to the Editor/Carbon, Vol. 41, pp. 1325-1328, 2003.
7. C. A. Cooper, D. Ravich, D. Lips, J. Mayer and H. D. Wagner. “Distribution and Alignment of Carbon Nanotubes and Nanofibrils in a Polymer Matrix,” Composites Science and Technology, Vol. 62, pp. 1101-1102, 2002.
8. M. Wong, M. Paramsothy, X. J. Xu, Y. Ren, S. Li and K. Liao, “Physical Interactions at Carbon Nanotube-polymer Interface,” Polymer, Vol. 44, pp. 7757-7764, 2003.
9. K. T. Lau, “Interfacial Bonding Characteristics of Nanotube/polymer Composites,” Chemical Physical Letter, Vol. 370, pp. 399-405, 2003.
10. E. T. Thostenson and T. W. Chou, “Nanotube Buckling in Aligned Multi-wall Carbon Nanotube Composites,” Carbon, Vol. 42, pp. 3015-3022, 2004.
11. D. S. Lim, J. W. An and H. J. Lee, “Effect of Carbon Nanotube Addition on the Tribological Behavior of Carbon/Carbon Composite,” Wear, Vol. 252, pp. 512-517, 2002.
12. M. K. Yeh, N. H. Tai and Y. J. Lin, “Fabrication and Mechanical Properties of MWNTs/Phenolic Nanocomposites,” 2005 International Conference on Advanced Manufacture, Taipei, Taiwan.
13. X. Z hou, E. Shin, K. W. Wang and C. E. Bakis, “Interfacial Damping Characteristics of Carbon Nanotube-based Composite,” Composites Science and Technology, Vol. 64, pp. 2425-2437, 2004.
14. I. C. Finegan, G. G. tibbetts and R. F. Gibson, “Modeling and Characterization of Damping in Carbon nanofiber/polypropylene Composites,” Composites Science and Technology, Vol. 63, pp.1629-1635, 2003.
15. N. A. Koratkar, B. Wei and P. M. Ajayan, “Multifunctional Structural Reinforcement Featuring Carbon Nanotube Films,” Composites Science and Technology, Vol. 63, pp. 1525-1531, 2003.
16. C. A. Steevens and N. A. Flect, “Material Selection in Sandwich Beam Construction,” Scripta Materialia, Vol. 50, pp. 1335-1339, 2004.
17. J. Kim and S. R. Swanson, “Design of Sandwich Structures for Concentrated Loading,” Composite Structure, Vol. 52, pp. 365-373, 2001.
18. A. Muc and P. Zuchara, “Buckling and Failure Analysis of FRP Face Sandwich Plates,” Composite Structure, Vol. 40, pp. 145-150, 2000.
19. S. J. Huang, “An Analytical Method for Calculating the Stress and Strain in Adhesive Layers in Sandwich Beams,” Composite Structures, Vol. 60, pp. 105-114, 2003.
20. Y. W. Kwon, S. H. Yoon and P. J. Sistare, “Compressive Failure of Carbon-Foam Sandwich Composites with Holes and/or Partial Delamination,” Composites Structures, Vol. 38 pp. 573-580, 1997.
21. W. J. Cantwell, R. Scudamore, J. Ratcliffe and P. Davies, “Interfacial Fracture in Sandwich Laminates,” Composites Science and Technology, Vol. 59, pp. 2079-2085, 1999.
22. J. H. Yim, S. Y. Cho, Y. J. Seo and B. Z. Jang, “A Study on Material Damping of 0° Laminated Composite Sandwich Cantilever Beams with a Viscoelastic Layer,” Composite Structures, Vol. 60, pp. 367-374, 2003.
23. S. A. Nayfeh, “Damping of Flexural Vibration in the Plane of Lamination of Elastic-Viscoelastics Sandwich Beams,” Journal of Sound and Vibration, Vol. 276, pp. 689-711, 2004.
24. L. Kari, K. Lindgren, L. Feng and A. Nilsson, “Constrained Polymer Layers to Reduce Noise: Reality or Fiction-An Experimental Inquiry into their Effectiveness,” Polymer Testing, Vol. 21, pp. 949-958, 2002.
25. M. D. Rao, R. Echempati and S. Nadella, “Dynamic Analysis and Damping of Composite Structures Embedded with Viscoelastic Layers,” Composites, Vol. 28, pp. 547-554, 1997.
26. T. L. Teng and N. K. Hu, “Analysis of Damping Characteristics for Viscoelastic Laminated Beams,” Computer methods in applied mechanics and engineering, Vol. 190, pp. 3881-3892, 2001.
27. W. Y. Jung and A. J. Aref, “A Combined Honeycomb and Solid Viscoelastic Material for Structural Damping Application,” Mechanics of Materials, Vol. 35 pp. 831-844, 2003.
28. J. A. Zapfe and G. A. Lesieutre, “A Discrete Layer Beam Finite Element for the Dynamic Analysis of Composite Sandwich with Integral Damping Layers,” Computers and Structures, Vol. 70, pp. 647-666, 1999.
29. R. D. Corsaro and L. H. Sperling, Sound and Vibration Damping with Polymers, American Chemical Society, Washington, 1990.
30. P. Q. Zhang, J. H. Ruan and W. Z. Li, “Influence of Some Factors on the Damping Property of Fiber-reinforced Epoxy Composites at Low Temperature,” Cryogenics, Vol. 41, pp. 245-251, 2001.
31. A. S. Hadi and N. Ashton, “Measurement and Theoretical Modelling of the Damping Properties of a Uni-directional Glass/epoxy Composite,” Composite Structures, Vol. 34, pp. 381-385, 1996.
32. T. R. Lin, N. H. Farag and J. Pan, “Evaluation of Frequency Rubber Mount Stiffness and Damping by Impact Test,” Applied Acoustics, Vol. 66, pp. 829-844, 2005.
33. M. D. Rao, “Recent Applications of Viscoelastic Damping for Noise Control in Automobiles and Commercial Airplane,” Journal of Sound and Vibration, Vol. 262, pp. 457-474, 2003.
34. H. Fukudome, K. Nakazato and Y. Aoi, “The Study on Application of High Damping Adhesive to Body Joint Location,” Mitsubushi Motors Corporation, Vol. 12, pp. 81-84.
35. A. Kaya, M. S. Tekelioglu and F. Findil, “Effects of Various Parameters on Dynamic Characteristics in Adhesively Bounded Joints,” Materials Letters, Vol. 58, pp. 3451-3456, 2004.
36. X. Boutillon and B. David, “Assessing Tuning and Damping of Historical Carillon Bells and their Changes Through Restoration,” Applied Acoustics, Vol. 63, pp. 901-910, 2002.
37. J. Bretos, C. Santamaria and J. A. Moral, “Finite Element Analysis and Experimental Measurements of Natural Eigenmodes and Random Responses of Wooden Bars Used in Musical Instruments,” Applied Acoustics, Vol. 56, pp.141-156, 1999.
38. ANSYS Element Reference. 000855. Eighth Edition. SAS IP, Inc.1997
39. ANSYS Theory Reference. 000855. Eighth Edition. SAS IP, Inc.1997
40. R. F. Gibson, Principles of Composite Material Mechanics, McGraw-Hill, New York, 1994.
41. S. S. Rao, Mechanical Vibrations, Pearson Prentice Hall, 2004.
42. A. D. Nashif, D. I. G. Jones and J. P. Henderson, Vibration Damping, Wiley, New York, 1985.
43. 林奕男, 懸臂樑結構尺寸與自然頻率及阻尼比關係之研究,” 中興大學機械工程研究所論文, 2004.
44. ASTM E756-98, “Standard Test Method for Measuring Vibration-Damping Properties of Materials”, Annual Book of ASTM Standards, 1998.
45. 林彥君, “以多壁奈米碳管及纖維補強酚醛樹脂之複合材料機械性質研究,” 清華大學動力機械工程研究所論文, 2005.
46. K. S. Kim and C. S. Hong, “Delamination Growth in Angle-Ply Laminated Composites,” Journal of Composite Materials, Vol. 20, pp. 423-438, 1986.
47. M. K. Yeh and C. M. Tan, “Buckling of Elliptically Delaminated Composite plates,” Journal of Composite Materials, Vol. 28, No. 1, pp. 36-52, 1994.
48. ASTM D3039-76, “Standard Test Method for Tensile Properties of Fiber-Resin Composites,” Annual Book of ASTM Standards, Section 3, Vol. 15.03, pp. 162-165, 1983.
49. ASTM D3518-76, “Standard Practice for Inplane Shear Stress-strain Response of Unidirectional Reinforced Plastics,” Annual Book of ASTM Standards, Section 3, Vol. 15.03, pp. 202-207, 1983.
50. L. A. Carlsson and R. B. Pipes, Experimental Characterization of Advanced Composite Materials, New Jersey, Prentic-Hall, 1987.
51. ASTM D638-82a, “Standard Test Method for Tensile Properties of Plastics,” Annual Book of ASTM Standards, Vol. 8.2, 1982.
52. J. W. Dally and W. F. Riley, “Experimental Stress Analysis,” New York, McGraw-Hill Inc., 1991
53. 劉增豐, “高強度高韌性鐵鋁錳合金鋼之研製,” 科學發展月刊, 第28卷, 第12期, pp. 943-946.