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研究生:蕭詩旋
研究生(外文):Shiau-Shr Shiuan
論文名稱:運用壓電吸振器於旋轉雷力夫樑上之減振設計
論文名稱(外文):DESIGN OF PIEZOELECTRIC ABSORBERS FOR REDUCING VIBRATION OF ROTATING RAYLEIGH BEAM
指導教授:黃以玫黃以玫引用關係
指導教授(外文):Yii-Mei Huang
學位類別:碩士
校院名稱:國立中央大學
系所名稱:機械工程研究所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:中文
論文頁數:93
中文關鍵詞:旋轉雷力夫樑壓電吸振器裝置
外文關鍵詞:rotating Rayleigh beampiezoelectric absorber
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本文的主要目的為探討壓電吸振器應用於旋轉雷立夫樑的減振效應。本文系統考慮兩端為簡支撐的旋轉雷立夫樑,樑上受到一簡諧外力激振,並假設外力頻率與樑轉動速度相等。文中將壓電材料貼附於旋轉雷立夫樑表面上,並配合適當的電子元件與電路,形成一對於系統具減振效果的壓電吸振器裝置,因此當旋轉雷立夫樑受外力激振產生振動時,則即可用壓電吸振器來抑制系統過大的振動量。

本文根據漢米爾頓定理推導出旋轉雷立夫樑貼上壓電材料的系統運動方程式,並配合壓電吸振器的電路方程式形成一偏微分方程組,再利用格勒金法將系統運動方程式離散化,求出系統的位移解,並由數值結果加以分析討論,進而得知壓電吸振器對系統減振特性。
The purpose of this thesis was to use the piezoelectric absorber for reducing the vibration of dynamics of a rotating Rayleigh beam. The general model was a rotating Rayleigh beam with simply supported ends subject to the external harmonic force. The beam was bonded on the surface with piezoelectric absorbers. It was assumed that the frequency of the external harmonic force was equal to the rotating frequency of the beam. Because piezoelectric material was shunted with a resistor and an inductor was similar to a mechanical vibration absorber, this type of piezoelectric absorbers could reduce the large vibration of rotating system.

The equations of motion of the composite rotating beam were derived by Hamilton’s principle and decretized by Galerkin’s method. The dynamic response of the beam subjected to the harmonic force was solved. Various designs of the absorbers were discussed in this thesis. The numerical results show that the absorbers are effective for reducing the vibration of the rotating beam.
第一章 緒論……………………………………………………………1
1.1 研究動機………………………………………………………1
1.2 文獻回顧………………………………………………………2
1.3 內容架構………………………………………………………4
第二章 系統運動方程式………………………………………………5
2.1 壓電材料理論…………………………………………………5
2.1-1 壓電現象…………………………………………………5
2.1-2 壓電材料種類……………………………………………6
2.1-3 壓電材料性質……………………………………………7
2.2 系統運動方程式之推導………………………………………7
2.2-1 基本假設…………………………………………………7
2.2-2 漢米爾頓定理與系統動能、位能、外力功……………8
2.2-3 運動方程式………………………………………………13
2.3 壓電吸振器電路方程式之推導………………………………16
第三章 運動方程式近似解……………………………………………20
3.1 運動方程式離散化……………………………………………20
3.2 運動方程式位移響應…………………………………………24
第四章 數值結果討論…………………………………………………25
4.1 系統參數設定…………………………………………………25
4.2 自然頻率與零界轉速分析……………………………………25
4.2-1 原始系統自然頻率與臨界轉速分析……………………26
4.2-2 複合系統自然頻率與臨界轉速分析……………………28
4.3 系統受外力激振之位移解……………………………………29
4.3-1 單向外力…………………………………………….……30
4.3-2 雙向外力………………………………………………….31
4.4 調變壓電吸振器參數對系統之減振影響……………………33
4.4-1 調變壓電吸振器阻尼比對系統之減振影響……………34
4.4-2 調變壓電吸振器頻率對系統之減振影響………………35
4.5 改變吸振器貼附在旋轉樑上的位置對減振影響……………36
4.5-1 改變壓電吸振器在y-z平面上角度對系統的减振影響
……………………………………………………………36
4.5-2 改變壓電吸振器位置對系統之減振影響………………37

4.6 壓電吸振器同時對第一、二模態兩向前進動共振頻率之幅值減振影 響………………………………………………………39
4.7 多組壓電吸振器對系統受單向外力激振下不同模態的減振影
響………………………………………………………………41
第五章 結論與未來建議……………………………………………46
5.1 結論整理……………………………………………………46
5.2 未來建議……………………………………………………49
參考文獻………………………………………………………………50
作者簡介………………………………………………………………72
吳朗, 1994,”電子陶瓷-壓電,”全新科技出版社,台北市.

陳琮仁, 2004, 旋轉樑的動態分析與壓電吸振器之減震設計, 國立中央大學機械工程研究所碩士論文, 桃園縣.

Bauer, H. F., 1980, “Vibration of a Rotating Uniform Beam, Part I: Orientation in the Axis of Rotation”, Journal of Sound and Vibration, Vol. 72, pp. 177—189.

Cheng, C. C. and Lin, J. K., 2003, “Modelling a Rotating Shaft Subjected to a High-speed moving force”, Journal of Sound and Vibration, Vol. 261, pp. 955—965.

Dimitriadis, E. K., Fuller, C. R., and Rogers, C. A., 1991, “Piezoelectric Actuators for Distributed Vibration Excitation of Thin Plate”, Journal of Vibration and Acoustics, Vol. 113, pp. 100—107.

Filipich, C. P., Maurizi, M. J., and Rosales, M. B., 1987, “Free Vibrations of a Spinning Uniform Beam with Ends Elastically Restrained against Rotation”, Journal of Sound and Vibration, Vol. 116, pp. 475—482.

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Zu, Jean W. Z. and Han, Ray P. S., 1992, “Natural Frequencies and Normal Modes of a Spinning Timoshenko Beam with General Boundary Conditions”, ASME Journal of Applied Mechanics, Vol. 59, pp. S197—S204.
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