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研究生:劉忠義
研究生(外文):Jhong-Yi Liou
論文名稱:直桿受端點推力的後挫曲行為
論文名稱(外文):Post-buckling behavior of a rod under end thrust
指導教授:陳振山陳振山引用關係
指導教授(外文):Jen-San Chen
口試委員:單秋成莊嘉揚
口試委員(外文):Chow-Shing ShinJia-Yang Juang
口試日期:2015-06-03
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:機械工程學研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2015
畢業學年度:103
語文別:中文
論文頁數:82
中文關鍵詞:彈性桿件振動大變形理論
外文關鍵詞:elastic theoryvibrationdirector
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在本文中,主要研究桿件一端夾持於可自由旋轉的軸承上,另一端夾持於可移動的滑車,使其可以沿線性軌道作無摩擦滑動在軸承施予固定的扭力後,在給予軸向力,探討整個移動過程中桿件的變形。本文使用空間彈性理論來分桿件的靜態變形與振動頻率,將其視為一個邊界值的問題,並利用Shooting Mehhod來求解,求解到靜態解後,再經由振動分析來探討各個靜態解的穩定性,接著,我們也設計了一組實驗機構,由此來驗證我們的結果是否正確,另外,本文也將探討彈性桿件加上初始扭率後,對臨界負載的影響,從elastica控制方程式開始進行理論推導,求出其曲率及位移的通解,將通解帶入邊界條件求出在不同邊界條件下的特徵方程式,再由數值方法做計算來加以比對,本文將討論Spherically-Hinged的邊界以及clamped-clamped的邊界,將此視為一個特徵值的問題進行臨界負載分析,並針對初始扭率很大的特殊情況下來進行討論。

In this paper we use elastic theory to study the deformation and natural frequencies of a rod. We consider a rod with circular section. One clamp is fixed with freely rotating bearing , and the other is attached to a slider which is allowed to slide without friction on a linear track. We study the post- buckling behavior and static deformation of a rod elastica by using shooting method. There are lots of static deformation of a rod elastica under axial thrust as we predict. Determine stability of each static deformation by perturbation theory. Moreover, we derive characteristic equation from governing equation of pre-rotated elastica to obtain critical load. We will discuss two different boundary conditions in this paper including spherically-hinged and clamped-clamped and the effect on different properties of elastica such as infinite initial torsion.

第一章 導論 1
第二章 理論模型與控制方程式 3
2.1彈性直桿理論模型 3
2.2控制方程式與推導過程 3
第三章 靜態變形分析 8
第四章 振動分析 12
4.1無自我接觸桿件振動分析 12
4.2自我接觸桿件振動分析 14
第五章 受力與位移關係分析 24
第六章 穩定性分析 26
第七章 實驗設計 28
第八章 臨界附載分析臨界 30
8.1 Spherically-Hinged 32
8.2 Clamped-Clamped 34
第九章 結論 38
參考文獻 40
附錄I 73
附錄II 75
符號表 80


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