具有翼動角的旋轉葉片常是被設計的，但是很少文獻探討翼動角在振動上的影響。本文研究具安置角和翼動角的旋動Timoshenko樑的振動和發散不穩定。利用漢米頓原理推導出旋轉Timoshenko樑的耦合統御微分方程式和其邊界條件。在不考慮軸向伸長和科氏力效應的情況下，當樑的幾何性質和材料性質可以表示成多項式形式，樑的精確解可以求得。
在本文中，呈現了旋轉Timoshenko樑參數之間的一些簡單的關係式。基於這些關係式，從一已知參數的系統可以預測另一未知系統的自然頻率和參數。並且研究旋轉的發散不穩定(拉伸挫曲)。本文探討了翼動角和其它物理參數對自然頻率的影響和發散不穩定的現象。

A rotating blade with a flapping angle is usually designed, but little literature investigated the effect of the flapping angle on vibration. This paper investigates divergent instability and vibration of a rotating Timoshenko beam with flapping and setting angles. It uses Hamilton's principle to derive the coupled governing differential equations and the boundary conditions for a rotating Timoshenko beam. Without considering the extension in the axial direction and the Coriolis forces effect , the probles's exact solution can be obtaind if the beam's geometric and material properties can be writtren into polynomial forms.
Some simple relations among the parameters of a rotating Timoshenko beam are revealed. Based on these relations, one can predict the natural frequencies and the parameters of another system from those of one known system. Moreover, the mechanism of divergent instability (tension buckling) is investigated. Finally, the influences of the flapping angle and other physic parameters on the natural frequencies, and the phenomenon of divergence instability are investigated.

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