陳振山臺灣大學：機械工程學研究所謝文雄Hsieh, Wen-HsiungWen-HsiungHsieh2007-11-282018-06-282007-11-282018-06-282005http://ntur.lib.ntu.edu.tw//handle/246246/61141本文是以實驗與理論的方式來探討圓桿扭轉挫曲的現象。首先以Love提出的直桿平衡方程式為基礎，在直桿的變形位移很小的假設下，將平衡方程式化成以側向變形表示的兩條方程式。平衡方程式中的曲率是以隨體座標表示的位移函數來表示。以此方程式求出的臨界扭矩與傳統Ziegler在忽略截面扭角下求出的值相同。實驗上是設計一組實驗機構，可以同時對桿施加軸向壓力與扭矩，再以長2.73 m、直徑4.4 mm的鋁條來做實驗。桿的兩端是夾持但有一端可在軸向自由滑動。實驗時是先施加固定的軸向壓力，再緩緩的施加扭矩，並紀錄下扭角與端點的位移變化。當挫曲時，滑動端會產生跳動收縮的現象。當軸向壓力愈大，也就是臨界扭矩愈小時，臨界負載與扭角的實驗結果就與理論預測值愈近，實驗值比理論值小在10％以內。當只受扭矩時，誤差值最大，誤差有超過20％。造成實驗誤差的原因，在文中有詳細的討論。In this thesis we study, both experimentally and analytically, the torsion buckling of a rod with circular cross section. In the analysis we start with the general equilibrium equations for a straight rod formulated by Love. These equilibrium equations are simplified to two equations in terms of the lateral deflections by considering the situation when the rod is only slightly different from the straight configuration. The key to this derivation is to formulate the correct form of curvatures in terms of the lateral deflections relative to a body-fixed coordinate system. The resulted critical torque is found to be identical to the classical critical torque formulated by Ziegler by ignoring the pre-buckled twisting angle. In the experiment, we design a loading mechanism which allows us to apply the compressive force and torque at the same time. Commercially available aluminum rod with diameter 4.4 mm and length 2.73 m is tested in the experiment. Both ends of the rod are clamped while one end is allowed to slide axially freely. In the experiment we apply a specified compressive force first and then increase the end torque gradually. The axial displacement and the twist angle as functions of end torque are recorded. The critical torque is recognized as the torque at which the rod undergoes a sudden jump in the axial direction. Measured critical loads are compared with the analytical predictions. In the case when the compressive force is close to the Euler buckling load, the discrepancy between the measured critical torque and the theory is in the range of 10%. On the other hand, when the rod buckles solely due to torsion, the discrepancy between experiment and theory can be as high as 20%. The possible causes of the discrepancy are discussed in detail.第一章 導論..........................1 1.1 研究動機.........................1 1.2 文獻回顧.........................1 1.3 研究方法.........................4 第二章 理論分析......................5 2.1 平衡方程式.......................5 2.2 臨界挫曲負載與扭角..............11 2.3 挫曲形狀........................14 第三章 實驗設備與實驗結果...........18 3.1實驗架構與設備...................18 3.2臨界挫曲負載與扭角的量測.........20 3.3挫曲形狀的量測...................23 3.4實驗討論.........................24 第四章 結論.........................28 參考文獻............................30 附圖目錄............................311132415 bytesapplication/pdfen-US挫曲torsionbucklingthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/61141/1/ntu-94-R92522532-1.pdf