本文研究自由端具一集結質量之軸向移動及自旋懸臂樑的動態特性，並探討等速率伸長及週期性來回伸縮之兩種軸向移動型態對懸臂樑之動態特性的影響。首先，我們以考慮旋轉慣性的雷利樑(Rayleigh beam)理論為基礎，利用漢彌頓原理(Hamilton's principle)及具時變元素和非時變元素之有限元素法推導出系統之運動方程式。利用阮奇-庫達(Runge-Kutta)數值積分方法解出系統之振動響應，並討論質量塊之質量及轉動慣量對系統的頻率與響應的影響；並分別使用特徵值及傅羅凱理論(Floquet theory)來判別具軸向等速率伸長及週期性來回伸縮運動型態之軸向移動樑的穩定性，並由位移響應的分析結果來確認穩定性分析的正確性。

In this thesis, the dynamic characteristics of an axially moving and spinning Rayleigh beam with a tip mass is investigated. Two kinds of axial motion including constant-speed extension deployment and back-and-forth periodical motion are considered. Variable-domain finite-element models for the above system are developed by using Hamilton's principle for determination of natural frequencies, transient responses and stability. Direct time numerical integration, based on a Runge-Kutta algorithm, is used to perform the dynamic analysis. Influences of the tip mass on the natural frequency and dynamic response of the beam are discussed. For stability analysis, eigenvalues of motion equation of the beam with constant-speed axial extension deployment are obtained to determine its stability, while Floquet theory is employed to investigate the stability of the beam with back-and-forth periodical axially motion. Time histories are obtained to confirm the results from Floquet theory.

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