在本文中,主要研究桿件一端夾持於可自由旋轉的軸承上,另一端夾持於可移動的滑車,使其可以沿線性軌道作無摩擦滑動在軸承施予固定的扭力後,在給予軸向力,探討整個移動過程中桿件的變形。本文使用空間彈性理論來分桿件的靜態變形與振動頻率,將其視為一個邊界值的問題,並利用Shooting Mehhod來求解,求解到靜態解後,再經由振動分析來探討各個靜態解的穩定性,接著,我們也設計了一組實驗機構,由此來驗證我們的結果是否正確,另外,本文也將探討彈性桿件加上初始扭率後,對臨界負載的影響,從elastica控制方程式開始進行理論推導,求出其曲率及位移的通解,將通解帶入邊界條件求出在不同邊界條件下的特徵方程式,再由數值方法做計算來加以比對,本文將討論Spherically-Hinged的邊界以及clamped-clamped的邊界,將此視為一個特徵值的問題進行臨界負載分析,並針對初始扭率很大的特殊情況下來進行討論。
In this paper we use elastic theory to study the deformation and natural frequencies of a rod. We consider a rod with circular section. One clamp is fixed with freely rotating bearing , and the other is attached to a slider which is allowed to slide without friction on a linear track. We study the post- buckling behavior and static deformation of a rod elastica by using shooting method. There are lots of static deformation of a rod elastica under axial thrust as we predict. Determine stability of each static deformation by perturbation theory. Moreover, we derive characteristic equation from governing equation of pre-rotated elastica to obtain critical load. We will discuss two different boundary conditions in this paper including spherically-hinged and clamped-clamped and the effect on different properties of elastica such as infinite initial torsion.