受拘束拱梁在集中力矩作用下之穩定性分析

Abstract

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.