臺灣博碩士論文加值系統

本文對彈性介質內嵌入的單壁奈米碳管(single-walled carbon nanotube, SWCNT)在簡支與懸臂邊界上進行完整的力學分析。基於連體力學理論，以非局部Timoshenko梁建構理論模型，並以Winkler彈性支承模擬SWCNT與周圍介質間的作用力。在SWCNT自然振動行為中，基於虛位移原理(principle of virtual displacements, PVD)推導其弱形式方程式，並應用有限元素法與解析解做驗證，根據自然頻率的變化探討非局部效應對不同參數(模態、螺旋性、長徑比與周圍介質勁度)SWCNT造成的影響。在嵌入式Armchair (18,18) SWCNT受到外力的波傳行為中，建立射線法理論架構解得其轉換域下的理論解，並透過Durbin數值逆轉換求解時域下的暫態反應解，另一方面，應用模態疊加法將振動行為結果延伸至探討SWCNT的波傳行為，其反應解包含解析與數值解。將以上三種暫態結果相互比較驗證，得知，非局部效應使波傳反應變得平滑，且量測點未接收到波源傳遞便受到整體結構波傳作用而產生反應。

Dynamic behaviors of single-walled carbon nanotube (SWCNT) embedded in an elastic medium are studied on the basis of the nonlocal Timoshenko beam model. Free vibration of SWCNT is analyzed and verified by numerical and theoretical methods. Influences of the slender ratios, the boundary conditions, the atomic structures, and the stiffness of the embedded medium on the natural frequencies and mode shapes of SWCNT are also examined. In transient analysis, we use ray and normal mode approaches. The results are in good agreement. The nonlocal effect smooths the transient responses, Different from classical Timoshenko beam, the nonlocal Timoshenko beam model shows instantaneous wave propagation owing to the nonlocal effect.

摘要 I
Extended Abstract II
誌謝 VI
目錄 VII
表目錄 IX
圖目錄 X
符號表 XIV
第一章 緒論 1
1-1 文獻回顧 1
1-2 本文架構 5
第二章 奈米碳管的結構性質 6
第三章 SWCNT振動行為分析 8
3-1 Eringen非局部彈性理論 8
3-2 SWCNT控制方程式 9
3-3 SWCNT自由振動理論解 13
3-4 SWCNT自由振動數值解 22
第四章 SWCNT波傳行為分析 25
4-1 射線法 25
4-1-1 轉換域下的射線解 26
4-1-2 Durbin數值逆轉換 37
4-2 模態疊加法 41
4-2-1 時間函數求解 42
4-2-2 SWCNT的暫態理論解 46
4-2-3 SWCNT的暫態數值解 48
第五章 數值結果討論 49
5-1 SWCNT自由振動結果分析 49
5-2 SWCNT波傳行為結果分析 68
5-2-1 SWCNT在簡支邊界上的暫態反應 68
5-2-2 SWCNT在懸臂邊界上的暫態反應 70
第六章 結論與未來研究方向 86
6-1 結論 86
6-2 未來研究方向 87
參考文獻 88

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