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研究生:陳琮仁
研究生(外文):Tsung-Jen Chen
論文名稱:旋轉樑的動態分析與壓電吸振器之減振設計
論文名稱(外文):Dynamic modeling of a rotating Rayleigh beam bonded with piezoelectric absorbers
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:2004
畢業學年度:92
語文別:中文
論文頁數:95
中文關鍵詞:壓電吸振器旋轉樑
外文關鍵詞:rotating beampiezoelectricabsorber
相關次數:
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  • 下載下載:42
  • 收藏至我的研究室書目清單書目收藏:2
一般撓性結構在高速運轉時,容易受簡諧外力作用而產生橫向振動,如轉子偏心不平衡或裝置不對心所造成的離心力,產生過大的振幅,導致結構的破壞或受損,本文的主要目的即是探討壓電吸振器應用於旋轉樑的減振效應。
本文模擬一兩端簡支撐的雷立夫樑,在樑上受到一簡諧集中力激振,並假設外力頻率和轉動速度相等。文中分析此旋轉系統的動態特性,並嘗試將壓電材料貼附於旋轉樑表面,再配合電感、電阻與適當的電路,形成類似機械式吸振器的裝置。由於壓電材料具有機械能和電能互換的特性,當系統受力而產生變形與振動時,壓電材料會因應變而產生電場,其外加的電路會消耗因壓電材料變形產生了的電能,以減少系統的振動量。
本文是由能量法的觀點出發,根據漢米爾頓定理來推導旋轉樑貼上壓電材料的運動方程式,並配合壓電吸振器的電路方程式而形成一偏微分方程組,再利用格勒金法將系統離散化,求出系統的位移解,最後以數值模擬分析。本文採用被動式吸振器控制系統,文中分別針對壓電吸振器可調變的參數作探討,進而得知壓電吸振器對於系統減振的特性。
The forced vibration of a flexible beam rotating about its longitudinal axis is easy to produce excessive vibration and failure. In general, the external force is the centrifugal force caused by the unbalanced rotor or misalignment. The purpose of this study is to reduce the vibration of a rotating beam by using piezoelectric absorbers. Piezoelectric materials shunted with a resistor and an inductor is similar to a mechanical vibration absorber. The general model is a rotating Rayleigh beam, simply supported ends, surface-bonded with two pairs of piezoelectric absorbers.
The equations of motion of the composite rotating beam are derived by Hamilton’s principle and discretized by Galerkin’s method. The dynamic response of the model subjected to the harmonic force is solved. Various designs of the absorbers are discussed in this thesis. The numerical results show that the absorbers are effective for reducing the vibration of the
rotating beam.
目錄……………………………………………………………………I
圖索引…………………………………………………………………IV
表索引………………………………………………………………XI
符號說明………………………………………………………………XII
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 壓電材料之介紹………………………………………………5
2.1-1 壓電現象簡介……………………………………………5
2.1-2 壓電材料簡介……………………………………………6
2.1-3 壓電材料材料性質………………………………………7
2.2 系統運動方程式之推導………………………………………9
2.2-1 基本假設…………………………………………………9
2.2-2 漢米爾頓定理與系統動能、位能、外力功……………10
2.2-3 運動方程式………………………………………………14
2.3 壓電吸振器電路方程式之推導………………………………17
第三章系統近似解……………………………………………………21
3.1 系統離散化……………………………………………………21
3.2 系統位移響應…………………………………………………24
第四章數值結果討論…………………………………………………25
4.1 系統參數………………………………………………………25
4.2 原始系統的自然頻率與臨界轉速分析………………………26
4.3 改變壓電材料長度對自然頻率之影響………………………28
4.4 改變壓電材料位置對自然頻率之影響………………………30
4.5 壓電吸振器對自然頻率之影響………………………………30
4.6 系統受外力激振之位移解……………………………………31
4.6-1 單向外力…………………………………………………32
4.6-2 雙向外力,兩外力無相角差……………………………33
4.6-3 雙向外力,兩外力相角差90°…………………………33
4.7 改變壓電吸振器阻尼比對減振之影響………………………35
4.8 改變壓電吸振器頻率對減振之影響…………………………36
4.9 吸振器頻率對同一模態之兩共振頻率減振之影響…………37
4.10 改變壓電吸振器位置對不同模態減振之影響……………39
4.11 多組壓電吸振器對不同模態減振之影響…………………41
4.11-1 比較單組與雙組吸振器對第一模態之影響…………41
4.11-2 比較雙組與四組吸振器對不同模態之影響…………42
4.11-3 壓電吸振器對不同模態減振之設計…………………44
4.12 改變壓電吸振器長度對系統減振之影響…………………45
4.12-1 改變壓電吸振器長度對不同模態之影響……………45
4.12-2 壓電吸振器對系統減振之最佳設計…………………46
第五章結論與未來展望……………………………………………48
5.1 結論整理……………………………………………………48
5.2 未來展望……………………………………………………51
參考文獻………………………………………………………………53
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[2] 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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[8] 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.

[9] Nye, J. F., 1964, Physical Properties of Crystals, Oxford, Clarendon Press.

[10] Hagood, N. W. and von Flotow, A., 1991, “Damping of Structural Vibrations with Piezoelectric Materials and Passive Electrical Networks”, Journal of Sound and Vibration, Vol. 146, pp. 243—268.

[11] Hollkamp, J. J., 1994, “Multimodal Passive Vibration Suppression with Piezoelectric Materials and Resonant Shunts”, Journal of Intelligent Material Systems and Structures, Vol. 5, pp. 49—57.

[12] Wang, K. W., Yu, W. K., and Lai, J. S., 1994, “Adaptive-Passive Control of Structural Vibrations Via Piezoelectric Materials with Real-Time Adaptable Circuits”, Proceedings of Noise-Con 94, pp. 455—460.

[13] Park, C. H., 2003, “Dynamics Modelling of Beams with Shunted Piezoelectric Elements”, Journal of Sound and Vibration, Vol. 268, pp. 115—129.

[14] Yang, J. S. and Fang, H. Y., 2003, “A New Ceramic Tube Piezo- electric Gyroscope”, Sensors and Actuators A, Vol. 107, pp. 42—49.

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[17] Tiersten, H. F., 1969, Linear Piezoelectric Plate Vibrations, Plenum, New York.

[18] 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.
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