受彈簧牆拘束銷接樑的變形與振動分析

Abstract

本論文研究在一對溫克勒彈簧牆拘束下銷接樑的變形與振動分析，採用小變形理論。靜態分析表示挫曲樑與彈簧牆先呈現一線接觸，之後演變成兩線接觸。在力(邊緣推力)和位移(末端縮短量)關係圖中，存在一個最大邊緣推力。兩線接觸在此最大推力前後有明顯得不同。兩線接觸時，在邊緣推力到達最高點前，未接觸段的中點維持在彈簧牆附近。在超過最高點後，未接觸段的中點遠離彈簧牆直到中點碰到對面的彈簧牆。在振動分析中，本文考慮負載控制和位移控制，在負載控制下，變形達到最大邊緣推力前為穩定的，而經過最高點之後為不穩定的。在位移控制下，即使經過最大邊緣推力之後，變形也可保持穩定。對於反對稱型態的振動模態來說，自然頻率在負載控制和位移控制下都相同。對於對稱型態的振動模態來說，自然頻率在位移控制下一般都高於負載控制下的自然頻率。

In this paper we study the deformation and vibration of a pinned-pinned buckled beam constrained by a pair of springy walls of the Winkler type. Small deformation theory is adopted. Static analysis shows that the buckled beam contacts the springy wall in one segment first and then evolves to two-segment contact. In the edge thrust verses end shortening diagram, there exists a maximum edge thrust. The two-segment contact deformations before and after reaching the peak thrust are significantly different. Before reaching the peak, the free-of-contact segment in the middle stays close to the wall. After passing the peak, the free-of-contact segment moves away from the wall until the midpoint touches the opposite wall. In vibration analysis, both load control and displacement control are considered. In load control, the deformation before the edge thrust reaches its maximum is stable, while the one past the peak is unstable. In displacement control, the deformation may remain stable even after passing the maximum thrust. For anti-symmetric vibration modes, the natural frequencies are the same for load and displacement controls. For symmetric modes, the natural frequencies of displacement control are in general higher than the corresponding ones in load control.