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 本論文研究旋轉壓電葉片彈性支撐的動態分析。首先，利用Hamilton原理，推導出耦合統御微分方程式和具彈性邊界條件。尚未有學者針對本系統建構完整運動微分方程式模式。討論數學模式的特性和運動的相關性。因系統具有壓電控制，解微分方程式時，會出現複變數。一般非旋轉均勻樑具壓電片系統的運動微分方程式，其係數是常複數，屬於較簡單的問題，尚可解。但本系統方程式具複變係數，尚未有學者提出相關解析解。本論文提出一套方法，把複變數微分方程式分離成耦合實部和虛部方程式。將變換後微分方程式用矩陣表示之。推導複變係數微分方程式之矩陣半解析基本解，並推導矩陣基本解表示之特徵方程式。進一步，研究幾何性質、材料性質、控制條件、旋轉速度、邊界條件對自由頻率、穩定的影響。
 In this paper, the vibration of a rotating blade with piezoelectric element is investigated. First, the coupled governing partial differential equations and the elastic boundary conditions are derived by using Hamilton’s principle. Little research has been devoted to the vibration of a rotating piezoelectric blade with elastic boundary conditions. The features of the mathematical model are discussed. In general, the coefficients of the governing differential equations for a non-rotating uniform piezoelectric beam are constant complex. It is easy to derive the solution. But the coefficients of the system studied in this paper are complex variables. No analytical solution of the system is presented so far. In this paper, an analytical method is proposed. The differential equations with complex variables are divided into a real part and an imaginary one. The coupled differential equations are transformed to be in a matrix form. The frequency equation in a matrix form is derived. A semi-analytical fundamental solution for the system is derived. Moreover, the influence of the piezoelectric elements, rotating speed, control law, material and geometric properties on the frequencies and stability are investigated.
 中文摘要 i英文摘要 ii誌謝 iii目錄 iv表目錄 vi圖目錄 vii符號說明 viii一、緒論 11.1 前言 11.2 文獻回顧 21.3 研究動機及目的 31.4 本文架構 4二、統御方程式 62.1旋轉壓電樑的動能 72.2致動器和感測器的壓電關係 102.3旋轉壓電樑的位能 112.4統御方程式、邊界條件及初始條件 132.5無因次化統御方程式、邊界條件及初始條件 16三、旋轉壓電耦合樑的解析 203.1 統御方程式 203.2 解法 213.2.1複變數型式的特徵統御方程式、邊界條件和初始條件 223.2.2 頻率方程式 263.2.3 多項式型式 313.2.4 正合基本解 33四、數值分析 384.1特徵統御方程式、邊界條件和初始條件 384.2頻率方程式 414.3 正合基本解 434.4數值結果 47五、結論與建議 605.1 結論 605.2 建議 61參考文獻 62自述 67
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