陳振山臺灣大學：機械工程學研究所林勇志Lin, Yong-ZhiYong-ZhiLin2007-11-282018-06-282007-11-282018-06-282007http://ntur.lib.ntu.edu.tw//handle/246246/60999於本文將探討彈性板條的變形與穩定性，彈性板條的一端夾持住且固定於空間中，另一端同樣夾持住但角度不同於固定端，且可沿角度方向直線的自由滑動。在對滑動夾持端施以推力後，彈性板條會產生變形，我們觀察到當推力達到臨界值便會發生折斷式挫曲的現象，由原先的變形跳至另一穩定的變形；此外，希望以此結構傳遞運動或力量，故將對兩端的軸向力關係加以研究。在理論分析方面，針對幾種不同的固定夾持端與滑動夾持端之夾角，計算出靜態的受力-變形曲線以及軸向力傳遞關係；為了探討平衡位置的穩定性，在平衡位置加上微小的簡諧擾動，然後計算出彈性板條受力變形後的自然頻率；此外，對於兩端角度相同的情形，將有更深入的研究。我們設計一組實驗裝置以量測彈性板條的受力-變形曲線以及自然頻率；受力-變形曲線的量測結果與理論值相當吻合，而自然頻率的量測結果與理論值並不相符，但考慮滑動夾持端質量後，理論與實驗值相符許多。In this paper we study the deformation and stability of a planar elastica. One end of the elastica is clamped and fixed in space. The other end of the elastica is also clamped, but the clamp itself is allowed to slide along a linear track with a angle different from that of the fixed clamp. The elastica deforms after it is subject to an external pushing force on the moving clamp. It is observed that when the pushing force reaches a critical value, snapping may occur as the elastica jumps from one configuration to another remotely away from the original one. Moreover, in order to transfer motion or force by this structure, we will make a research into the relation between longitudinal forces of the two ends. In the theoretical investigation, we calculate the static load-deflection curves and the longitudinal forces transmission for a specified angle difference between the fixed clamp and the moving clamp. To study the stability of the equilibrium configuration, we superpose the equilibrium configuration with a small perturbation and calculate the natural frequencies of the deformed elastica. In addition, the condition where two ends with identical angles are introduced will be researched. An experimental set-up is designed to measure the load-deflection curve and the natural frequencies of the elastica. The measured load-deflection relation agrees with the theoretical prediction very well. On the other hand, the measured natural frequencies do not agree very well with the theoretical prediction, unless the mass of the moving clamp is taken into account.第一章 導論 1 第二章 理論模型與運動方程式 3 第三章 靜態變形分析 5 3.1 沒有反曲點的變形 5 3.2 兩個反曲點的變形 8 3.2.1 區段Ⅰ 8 3.2.2 區段Ⅲ 9 3.2.3 區段Ⅱ 10 3.3 一個反曲點的變形 11 3.4 之分析結果 12 3.4.1 受力-變形曲線(load-deflection curve) 12 3.4.2 反曲點位置變化 14 3.5 之受力-變形曲線 14 3.6 軸向力傳遞關係 15 第四章 自然頻率及穩定性分析 18 4.1 微擾法 18 4.2 Newton-Raphson method 20 4.3 自然頻率與穩定性分析 21 4.4 改變邊界條件為滑動端固定 23 第五章 直樑之分析 25 5.1 之挫曲後變形與穩定性分析 25 5.1.1 挫曲後的基本變形 25 5.1.2 挫曲後的其他變形 27 5.2 之變形 29 5.3 與 之關聯 30 第六章 實驗設備與量測 32 6.1 實驗設備 32 6.2 受力-變形曲線之量測 34 6.3 自然頻率之量測 34 6.3.1 實驗量測結果 35 6.3.2 理論修正-考慮滑動端質量 35 第七章 兩端夾角對折斷式挫曲之影響 37 第八章 結論 38 參考文獻 40 附圖目錄 431255068 bytesapplication/pdfen-US彈性板條大變形穩定性自然頻率折斷式挫曲elasticastabilitynatural frequencySnapthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/60999/1/ntu-96-R94522509-1.pdf