本文研究具翼動角旋轉樑的自由振動問題。首先，利用漢米頓原理及非線性樑理論，推導出耦合的特徵統御方程式。經過一連串的變數簡化過程，可獲得一條完全以撓曲位移所表示的變係數常微分方程式。若方程式中的變係數可用多項式來表示，則透過級數法，方程式的閉合基本解可被求得。
針對科氏力 (Coriolis force) 及軸向伸長的效應對旋轉樑的振動行為作探討。為了方便研究此兩種效應的影響，定義一無因次化旋轉軸向伸長參數；且透過圖示，科氏力及軸向伸長效應對旋轉樑自然頻率的影響由此表示出來。結果發現，若此參數較大，亦或旋轉樑的轉速較高時，科氏力及軸向伸長的效應將極為重要。
討論翼動角在旋轉樑自然頻率的影響。可發現到，對高轉速的旋轉樑而言，若翼動角較大，系統容易發生發散不穩定的機制。更進一步，亦評估及比較安置角、旋轉速度及輪轂半徑對旋轉樑自然頻率的影響。

In this study, the free vibration problem of a rotating beam with a flapping angle is investigated. First, by utilizing the Hamilton’s principle and the consistent linearization of the fully non-linear beam theory, the coupled characteristic governing differential equations are derived. After taking a series of variable elimination process, one sixth-order ordinary differential equation only in terms of transverse displacement with variable coefficients can be obtained. If the variable coefficients of the differential equation can be expressed in a polynomial form, the closed-form fundamental solution of the equation can be developed via the power series method.
Both the Coriolis force effect and the extensional deformation are taken into consideration to evaluate the vibrational behavior of a rotating beam. To analysis the two effects on a rotating beam, one dimensionless rotational extensional parameter is defined. It is used to illustrate the influence of Coriolis force effect and the extensional deformation on the natural frequencies of a rotating beam. One can find that if the dimensionless rotational extensional parameter is large, or the rotational speed of the beam is high, the Coriolis force effect and the extensional deformation have significance.
The influence of the flapping angle on the natural frequencies of a rotating beam is investigated. It is shown that if the flapping angle of a high-speed rotating beam is large, the mechanism of divergence instability (tension buckling) happens easily. Furthermore, the influences of the setting angle, the rotational speed and the hub radius on the natural frequencies of a rotating beam are illustrated and compared.

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