跳到主要內容

臺灣博碩士論文加值系統

(3.231.230.177) 您好!臺灣時間:2021/07/28 19:56
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果 :::

詳目顯示

我願授權國圖
: 
twitterline
研究生:林詩晟
研究生(外文):Shih-Sheng Lin
論文名稱:圓桿受端點扭矩下的後挫曲行為
論文名稱(外文):Post-Buckling Behavior of a Rod under End Torque
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:莊嘉揚單秋成
口試委員(外文):Jia-Yang JuangChow-Shing Shin
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:88
中文關鍵詞:彈性圓桿振動臨界扭矩
外文關鍵詞:elasticalarge deformationvibrationcritical torque
相關次數:
  • 被引用被引用:0
  • 點閱點閱:74
  • 評分評分:
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
本文研究桿件在兩端邊界為固定端,施予固定軸向力後再施予端點扭矩,找出其變形的趨勢,其中一固定端施予扭轉,另一固定端可滑動。本文將使用elastica模型來模擬彈性桿件的變形現象,其邊界值問題利用Shooting Mehhod來求解。求出靜態解後再利用振動法來決定各個平衡解的穩定性。文中將會提及兩種不同的軸向力以及兩種不同的材料參數設定,討論其不同的影響,並設計了一實驗機構驗證理論之靜態變形是否正確。而接著在探討桿件若未施予軸向力時其臨界扭矩,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是,在由數值方法求出其臨界扭矩,並考慮一些特殊的例子,本文包含兩種邊界條件:(1)Spherically-hinged (2)Clamped-clamped。影響臨界扭矩的參數包含桿件長寬比、剪力模數及初始扭率,分析各種參數對臨界扭矩的影響,其中將剪力模數假設為非常大時和前人的結果相符合。桿件有初始扭率其臨界扭矩會比沒有初始扭率來的大。若桿件其初始扭率相當大時,其臨界扭矩會趨近於一定值,和理論值相符合。

In this paper we study post-buckling behavior of a rod with both ends clamped. One end is unrotatable and fixed, the other end is rotatable and allowed to slide. Edge thrust is fixed and the end rotation is varied. Elastica model is adopted to take into account exact geometry in large deformation. Vibration method is then employed to determine the stability of the equilibrium solution. We discuss to two different edge thrust and two diffenrent material constant, then point out the difference. Also, we derive the equation for the critical moment of a spherically-hinged pre-twisted rod under axial moment. It is found that in the case when the cross section has unequal principal moments of inertia the pre-rotation caused by end moment cannot be ignored in calculating the critical moment. On the other hand, if the two principal moments of inertia are equal, such as circular or square cross section, both the pre-twist and pre-rotation have no effect on the critical moment. The resulted equation for critical moment can be considered as the extension of the well-known Greenhill’s formula.

第一章 導論 1
第二章 理論模型與控制方程式 3
2.1 彈性桿件理論模型 3
2.2 控制方程式推導 3
第三章 靜態變形分析 9
3.1無自我接觸 9
3.2自我接觸 12
第四章 振動分析 13
4.1無自我接觸 13
4.2自我接觸 16
第五章 扭矩與角度關係分析 25
5-1

[1]Nour-Omid, B., Rankin, C.C., 1991. Finite rotation analysis and consistent linearization using projectors. Computer Methods in Applied Mechanics and Engineering 93, 353-384.
[2]Miyazaki, Y., Kondo, K., 1997. Analytical solution of spatial elastica and its application to kinking problem. International Journal of Solids and Structures 34(27), 3619-3636.
[3]van der Heijden, G.H.M., Neukirch, S., Goss, V.G.A., Champneys, Thompson, J.M.T., 2003. Instability and self-contact phenomena in the writhing of clamped rods. Int. J. Mech. Sci. 45, 161-196.
[4]Goyal, A.G., Perkins, N.C., Lee, C. L., 2005. Nonlinear dynamics and loop formation in Kirchhoff rods with implications to the mechanics of DNA and cables Journal of Computational Physics 209, 371–389.
[5]Goyal, A.G., Perkins, N.C., Lee, C. L., 2008. Non-linear dynamic intertwining of rods with self-contact. International Journal of Non-Linear Mechanics 43, 65 – 73
[6]Fang, J., Chen, J.-S., 2013. Deformation and vibration of a spatial elastica with fixed end slopes. International Journal of Solids and Structures 50,824-831.
[7]Fang, J., Chen, J.-S., 2014. Deformation and vibration of a spatial clamped elastica with noncircular cross section. European Journal of Mechanics–A/Solids 47, 182-193.
[8]Goss, V.G.A., van der Heijden, G.H.M., van der Heijden, G.H.M., Neukirch, S., 2005. Experiments on snap buckling, hysteresis and loop formation in twisted rods. Experimental Mechanics 45, 101-111.
[9]Goto, Y., Li, X.-S., Kasugai, T., 1996. Buckling analysis of elastic space rods under torsional moment. Journal of Engineering Mechanics 122, 826-833.
[10]Yang, Y.-B., Yau, J.-D., 1989. Stability of pretwisted bars with various end torque, Journal of Engineering Mechanics 115, 671-688.
[11]Reismann, H., Pawlik, P.S., 1980. Elasticity: Theory and Applications, John Wiley & Sons, New York.
[12]Coleman, B.D., Dill, E.H., Lembo, M., Lu, Z., Tobias, I., 1993. On the dynamics of rods in the theory of Kirchhoff and Clebsch. Arch. Rational Mech. Anal. 121, 339-359.
[13]Goriely, A., Tabor, M., 1997. Nonlinear dynamics of filaments, I. Dynamical instability. Physica D 105, 20-44.


QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
無相關點閱論文