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    Please use this identifier to cite or link to this item: http://ir.lib.ksu.edu.tw/handle/987654321/6836


    Title: 自旋非線性預扭承受軸向負載非均勻Timoshenko樑之振動分析
    Vibration Analysis of a Spinning Non-linearly Pretwisted Nonuniform Timoshenko Beam Under Axial Loading
    Authors: 何星輝
    Keywords: 自旋
    非線性預扭
    Date: 2000-07-31
    Issue Date: 2009-12-31 15:29:53 (UTC+8)
    Abstract: 本研究針對自旋、非線性預扭、承受軸向力、非均勻Timoshenko 樑振動問題做一基礎性研究。首先在自旋、預扭座標上應用Hamilton 原理及Timoshenko 理論推導上述問題之統御方程式及邊界條件。其次對其四條互偶、變係數偏微方程式及邊界條件取微分轉換,吾人可求得遞歸型式之代數方程組,進而使用符號運算求解代數方程組,最後將其結果取反微分轉換吾人可求得多項式型式之頻率方程式。  在不同邊界條件下,應用上述論理分析的結果研究並討論非線性預扭角、自旋速率、軸向負載對非均勻Timoshenko 樑自然頻率的影響;並與自旋、線性預扭、承受軸向力、非均勻 Timoshenko 樑的研究報告做比較,了解兩者之差異性。更進一步探研如何利用非線性預扭角的分佈來改善或調整自然頻率。
    In this research, a basic study on vibration problems of a spinning, nonlinearly pretwisted non-uniform Timoshenko beam under axial loading is studied. First, on a spinning twist coordinate, applying Hamilton’s principle and Timoshenko beam theory, the governing equations and boundary conditions of the above-mentioned problem are derived. Second, taking differential transform on these four coupled differential Equations with variant coefficient and boundary conditions, we obtain a set of algebraic equations in recursive form. Moreover, we solve the algebraic equations by using symbolic computation. Last, taking inverse differential transform on these reeults, we obtain a frequency equation in polynomial form. Under different boundary conditions, applying the theoretic results mentioned above, we investigate and discuss the effects of non-linearly pretwisted angle, spinning speed and axial loading on the natural frequencies of non-uniform Timoshenko beams. Moreover, we compare the calculated results with the research report on a spinning, linearly pretwisted Timoshenko beam under axial loading and study the difference between them. Furthermore, we investigate how to modify or design natural frequencies by using non-linearly distributed pretwisted angle.
    Appears in Collections:[機械工程系所] 研究計畫

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