臺灣博碩士論文加值系統

本文旨在探討有拘束平面限制之拱梁受靜態集中力矩作用下的行為，探討平衡解及其穩定性並佐以實驗驗證。首先證明拱梁和拘束平面只有點接觸，並推導接觸點上應滿足的拘束條件。接著利用模態展開法，配合拱梁的平衡方程及拘束條件，求得平衡解，探討平衡解的形態隨外力和系統參數變化的情形。利用能量法判別平衡位置的穩定性，由此詳細探討系統的分歧行為。最後架置實驗裝置，驗證理論分析的結果。

This thesis studies the behavior of a pinned half-sine arch under static concentrated moments with a constraint plane. Equilibrium positions and the associated stability of the arch under different conditions are investigated thoroughly. First, we prove that the arch can only contact the constraint plane at discrete points. The constraint conditions at the contact points are then derived. The method of mode expansion is used to solve the governing equations together with the constraint equations for the equilibrium positions. Then the variation of the equilibrium positions with the applied load and the system parameters are examined in detail. A modified energy method is proposed to determine the stability of the equilibrium positions. According to this method, comprehensive bifurcation analysis are conducted. Finally, experimental apparatus is set up to validate the theoretical results.

口試委員審定書（於紙本上） i
誌謝 ii
摘要 iii
Abstract iv
第一章 導論 1
第二章 理論分析 4
2.1 運動方程式 4
2.2 接觸的形式 7
2.3 拘束方程式 9
第三章 平衡解分析 10
3.1 單集中力矩 10
3.1.1 無接觸 10
3.1.2 有接觸點 14
1. 無挫屈 16
2. 有挫屈 18
3.2 對稱集中力矩對 25
3.2.1 無接觸 26
3.2.2 有接觸點 28
1. 無挫屈 28
2. 有挫屈 32
第四章 穩定性分析 43
4.1 能量法 43
4.2 有拘束條件能量法 46
4.2.1 單接觸點 47
4.2.2 多接觸點 51
第五章 實驗分析 53
5.1 實驗設備 53
5.2 實驗方法 55
第六章 結果討論 57
6.1 單力矩 58
6.1.1 無挫屈 58
1. d=π/3 58
2. d=π/4 60
3. d=π/5 62
6.1.2 有挫屈 64
1. d=π/3 64
2. d=π/4 68
3. d=π/5 72
6.2 對稱力矩對 76
6.2.1 無挫屈 76
1. d=π/4 76
2. d=π/6 77
6.2.2 有挫屈 80
1. d=π/3 80
2. d=π/4 83
3. d=π/6 90
第七章 結論 97
附錄一 99
附錄二 102
參考文獻 105

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［3］陳聖傑，雙