本研究主體為兩端鉸接之多層相疊2D非線性樑(multi-layered-beam (MLB))，此樑之下方以三次方非線性彈簧支撐之， 以模擬多壁奈米碳管置放於彈性基材之振動行為。利用牛頓第二定律、三維尤拉角座標轉換和泰勒展開式的結合以得到運動方程，之後使用多尺度法( Method of multiple scales ，MOMS)分析系統於穩態固定點(Fix Points)各模態之頻率響應。首先研究單壁奈米碳管及多壁奈米碳管置放於彈性基材之內共振現象，後續將施加一顆奈米粒子(Nano partical)於碳管最上層當作減振器Tuned Mass Damper (TMD)，考慮粒子之各種質量、彈性係數、阻尼係數及位置之組合，以期達到避開I.R.及減振之效益。本文第二部份則為分析多層奈米碳管置於彈性基材之振動現象。利用MOMS分析各層CNT及各振動模態之頻率關係，以判斷內共振之可能性，最後以一Nano particle嘗試抑制此多層奈米碳管系統之振動現象。本研究將提供最佳Nano partical的質量比、彈性係數及阻尼係數，並建議可達到最佳減振效果之擺放位置。以做為產學界未來奈米研究之參考。

We considered the multi-walled carbon nanotubes (MWCNTs) with interlayer van der Waals forces resting on a nonlinear elastic foundation. A nano-particle was applied on the top layer of the tube which was modeled as a point load. The effects of the elastic foundation and the interlayer van der Waals forces on the nanotubes stability were studied. The vibration of the carbon nanotube (CNT) was simulated by a hinged-hinged nonlinear Bernoulli-Euler beam with stretching effect. We analyzed this nonlinear system using the method of multiple scales (MOMS). Fixed points plots were also used to facilitate the observation of internal resonance. This made it possible for us to study the influence of nonlinear vibrations of the elastic beam (the CNT). The internal resonance was found on a single carbon nanotube resting on an elastic foundation (the matrix). However, no internal resonance happened in the MWCNT system due to its complicate frequencies between the beams. This prompted us to add a nano particle as the tuned mass damper (TMD) on the elastic beam in order to suppress internal resonance and vibrations. We examined the influence of the mass and location of the TMD as well as damping and spring coefficients on the damping effects. Analysis data were presented in graphs, including 3D maximum amplitude plots of the modes and 3D maximum amplitude contour plots (3D MACPs). The characteristics of the position of the particle load on the nanotubes vibration were examined. The parameters of the elastic foundation, interlayer van der Waals forces, and the position of the particle load to induce the smallest vibration and the most stable condition were concluded. As far as we know, no previous study has employed combinations of this type of TMD to MWCNTs. Our approach to damping is comprehensive in practical applications.

目錄
目錄	III
第一章、緒論	1
一、1研究動機	1
一、2文獻回顧	2
一、3研究方法	6
第二章、理論模式之建立	8
二、1非線性運動方程式之推導	8
二、2非線性運動方程式之無因次化	12
二、3多尺度法( Method of multiple scales ，MOMS)	14
二、4系統模態分析	16
第三章、內共振條件分析	19
三、1單壁奈米碳管置放於彈性基材之內共振分析	19
三、1.1彈性係數k=2500時之系統頻率響應	23
三、1.2彈性係數k=876時之系統頻率響應	27
三、2多壁奈米碳管置放於彈性基材之內共振分析	32
三、2.1彈性係數k=876時之系統頻率響應	35
第四章、附加動態減振器之系統分析	41
四、1單壁奈米碳管減振系統之頻率響應分析	41
四、2多壁奈米碳管減振系統之頻率響應分析	44
第五章、結果與討論	48
五、1單壁奈米碳管減振效益分析	48
五、2多壁奈米碳管減振效益分析	52
第六章、結論	56
附錄(一)無因次化參數定義	58
附錄(二) 時間項通解之表示式	59
附錄(三) 多壁奈米碳管之矩陣通式	60
參考文獻	62
論文簡要版	93

表目錄
表格 1 SWCNT-激擾1st mode， 	66
表格 2 SWCNT-激擾1st mode， 	67
表格 3 SWCNT-激擾1st mode， 	68
表格 4 MWCNT-激擾第一層1st mode， 	69
表格 5 MWCNT-激擾第一層1st mode， 	70
表格 6 MWCNT-激擾第一層1st mode， 	71
表格 7 MWCNT-激擾第一層1st mode， 	72
表格 8 MWCNT-激擾第一層1st mode， 	73
圖目錄
圖 1多壁奈米碳管置放於彈性基材模型圖	74
圖 2具減震器之主體架構與邊界條件	74
圖 3 Freq.與k之關係曲線	75
圖 4 Freq.與k之關係曲線-放大橫軸	75
圖 5單層激擾第一模態Fixed Point圖	76
圖 6單層激擾第三模態Fixed Point圖	76
圖 7多層激擾第一層第一模態Fixed Point圖	77
圖 8多層激擾第一層第三模態Fixed Point圖	78
圖 9單層附加減振器時，激擾第一模態Fixed Point圖	79
圖 10單層附加減振器時，激擾第三模態Fixed Point圖	79
圖 11多層附加減振器時，激擾第一層第一模態Fixed Point圖	80
圖 12單層激擾第一模態， 	81
圖 13單層激擾第一模態， 	81
圖 14單層激擾第一模態， 	82
圖 15單層激擾第一模態附加減振器， 	83
圖 16單層激擾第一模態附加減振器， 	83
圖 17主體樑之第一、第三模態示意圖	84
圖 18單層附加減振器之第一模態， 、 	85
圖 19多層激擾第一層第一模態， 	86
圖 20多層第一層第一模態， 	86
圖 21多層第一層第一模態， 	87
圖 22多層第一層第三模態， 	87
圖 23多層第一層第三模態， 	88
圖 24第一層第一模態附加減振器， 	89
圖 25第一層第一模態附加減振器， 	89
圖 26第一層第三模態附加減振器， 	90
圖 27第一層第三模態附加減振器， 	90
圖 28多層附加減振器之第一層第一模態， 、 	91
圖 29多層附加減振器之第一層第三模態， 、 	92

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