臺灣博碩士論文加值系統

本文主要討論以自感式壓電吸振器抑制旋轉雷利夫樑的振動效果，考慮旋轉樑為簡支撐邊界條件，外力部分受到一固定簡諧集中力，外力頻率假設與旋轉樑轉速相同。在旋轉樑的表面成對貼附壓電材料並且外接適當的電子電路，形成一具有吸振效果的壓電吸振器。本文在電路部份以惠斯登電橋電路為基礎，設計出同時具有感測和制動作用的自感式壓電吸振器電路，利用自感式壓電吸振器改善旋轉樑因外力激振而產生的振動現象。
首先使用漢米爾頓定理推導旋轉雷利夫樑與壓電材料之耦合運動方程式，再推導自感式壓電吸振器電路方程式，將兩組方程式聯立後用格勒金法將方程式簡化成僅與時間相關之常微分方程式，經過數值方法計算後得到複合旋轉樑系統之位移響應，進一步繪製位移響應圖形並作分析和討論。
本文的自感式壓電吸振器考慮電路中的電阻和電感分別為串聯和並聯兩種連接方式，由模擬結果得到兩種壓電吸振器皆須調整吸振頻率為樑之共振頻率才能得到不錯的吸振效果，對於抑制旋轉樑的振動，自感式電阻-電感並聯壓電吸振器較佳。

To reduce vibration of a rotating Rayleigh’s beam by using self- sensing piezoelectric absorbers was studied. The beam is simply supported and subjected to an external harmonic force with the frequency equal to rotating speed of the beam. Piezoelectric sheets each with a properly design electric circuit were attached to the beam to form self-sensing dynamic absorbers. Two types of piezoelectric circuits, series type and parallel type, were considered.
The equation of motion of the rotating, composite beam was derived by applying Hamilton ’s principle. The equations of circuits were also obtained. Combining these two types of equations and using Galerkin’s method can give the solution of beam vibration. The numerical results showed that reducing vibration of a rotating beam by the self-sensing piezoelectric absorber is effective. Parameter studies are also preformed.

中文摘要 ………………………………………………………… i
英文摘要 ………………………………………………………… ii
誌謝 ………………………………………………………… iii
目錄 ………………………………………………………… iv
圖目錄 ………………………………………………………… vii
表目錄 ………………………………………………………… xix
符號說明 ………………………………………………………… xx
第一章 緒論..........................................1
1.1 前言......................................... 1
1.2 文獻回顧..................................... 2
1.3 內容架構..................................... 4
第二章 壓電材料理論................................. 5
2.1 壓電現象..................................... 5
2.2 壓電材料種類................................. 6
2.3 壓電材料方程式................................7
第三章 系統之運動方程式與近似解..................... 9
3.1 基本假設..................................... 9
3.2 漢米爾頓定理與系統之動能、位能和外力功....... 10
3.3 壓電電壓之近似求解........................... 15
3.4 運動方程式................................... 16
3.5 系統運動方程式之近似解........................19
第四章 壓電吸振器之電路方程式........................23
4.1 基本壓電吸振器之組成..........................23
4.2 自感式電阻-電感串聯壓電吸振器................ 24
4.2.1 自感式電阻-電感串聯壓電吸振器電路之電路模式...24
4.2.2 自感式電阻-電感串聯壓電吸振器與旋轉樑系統結合之近
似解..........................................28
4.3 自感式電阻-電感並聯壓電吸振器.................29
4.3.1 自感式電阻-電感並聯壓電吸振器電路之電路模式...29
4.3.2 自感式電阻-電感並聯壓電吸振器與旋轉樑系統結合之近
似解......................................... 32
第五章 複合旋轉樑系統之數值結果和分析............... 34
5.1 系統參數設定................................. 34
5.2 旋轉樑之自然頻率與臨界轉速....................34
5.3 複合旋轉樑系統之外力形式......................37
5.3.1 單向之外力形式................................37
5.3.2 雙向之外力形式............................... 38
5.4 自感式電阻-電感串聯壓電吸振器之數值結果與分析 39
5.4.1 吸振頻率等於系統之共振頻率................... 40
5.4.2 吸振頻率不等於系統之共振頻率..................40
5.4.3 吸振頻率對稱於系統之共振頻率..................41
5.4.4 吸振頻率不對稱系統之共振頻率..................42
5.4.5 小結..........................................43
5.4.6 調整壓電材料位置之影響........................44
5.4.7 自感式電阻-電感串聯壓電吸振器在不同放大倍率之感應
電壓..........................................45
5.5 自感式電阻-電感並聯壓電吸振器之數值結果與分析 45
5.5.1 吸振頻率等於系統之共振頻率....................46
5.5.2 吸振頻率不等於系統之共振頻率..................47
5.5.3 吸振頻率對稱於系統之共振頻率..................48
5.5.4 吸振頻率不對稱系統之共振頻率................. 49
5.5.5 小結......................................... 49
5.5.6 調整壓電材料位置之影響........................50
5.5.7 自感式電阻-電感並聯壓電吸振器在不同放大倍率之感應
電壓..........................................51
5.6 自感式電阻-電感串聯壓電吸振器控制多模態之討論.52
5.7 自感式電阻-電感並聯壓電吸振器控制多模態之討論 52
5.8 兩種自感式壓電吸振器之結果比較............... 53
第六章 結論與建議....................................56
6.1 結論整理..................................... 56
6.2 未來建議..................................... 57
參考文獻 ............................................. 59
附錄.................................................. 61

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