直桿受端點推力的後挫曲行為

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。

關鍵字

彈性桿件；振動；大變形理論

並列摘要

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.

並列關鍵字

elastic theory ； vibration ； director

參考文獻

[1] Nour-Omid, B., Rankin, C.C., 1991. Finite rotation analysis and consistent linearization using projectors. Computer Methods in Applied Mechanics and Engineering 93, 353-384.

[2] Miyazaki, Y., Kondo, K., 1997. Analytical solution of spatial elastica and its application to kinking problem. International Journal of Solids and Structures 34(27), 3619-3636.

[3] van der Heijden, G.H.M., Neukirch, S., Goss, V.G.A., Champneys, Thompson, J.M.T., 2003. Instability and self-contact phenomena in the writhing of clamped rods. Int. J. Mech. Sci. 45, 161-196.

[4] Goyal, A.G., Perkins, N.C., Lee, C. L., 2005. Nonlinear dynamics and loop formation in Kirchhoff rods with implications to the mechanics of DNA and cables Journal of Computational Physics 209, 371–389.

[5] Goyal, A.G., Perkins, N.C., Lee, C. L., 2008. Non-linear dynamic intertwining of rods with self-contact. International Journal of Non-Linear Mechanics 43, 65 – 73

國際替代計量

直桿受端點推力的後挫曲行為

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