自感式壓電吸振器之設計與應用於矩形板之減振

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蕭勝聰(Sheng-Tsung Hsiao) 查詢紙本館藏

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機械工程學系

論文名稱

自感式壓電吸振器之設計與應用於矩形板之減振

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摘要(中)

本文考慮壓電材料具有機械能與電能互換特性，並應用惠斯登電橋原理，將壓電材料外接電路使其具有自我感應功能之壓電吸振器以控制矩形板之振動。
首先引用漢米爾頓定理及對薄板與壓電材料的基本假設，求出板與壓電材料偶合後之運動方程式；之後配合不同外加電路，設計出三種自感式壓電吸振器，並導出吸振器之電路方程式；最後由系統運動方程式與電路方程式並配合葛勒金近似法求出系統位移解，並將所得之數值結果加以分析討論。

摘要(英)

Recently, piezoelectric technology has been widely applied to large numbers of industrial devices because of its versatility in both sensors and actuators. In this study, a technique which allows a single piece of piezoelectric material to concurrently sense and actuate in a closed loop system will be applied to control the vibrations of the rectangular elastic plate which is simply supported. The piezoelectric material connected to the specific elastic circuit can serve as an absorber in the dynamic system. Theoretical bases for the thin plate and piezoelectric materials are cited to derive the governing equations of the system first. In a practical implementation of the self-sensing absorbers, an electrical bridge circuit composed of inductances, resistances and capacitances is designed to measure the output signal. Circuit equations and governing equations are provided to obtain the system response.
Numerical solutions show that two types of the circuits designed can be adopted for the absorbers. The main factors which influence the efficiency of the absorbers contain the area of the piezoelectric materials, the absorber resonant frequency, the damping ratio, and the feedback control gain. Simulations compared with other two control arguments, velocity feedback control and position feedback control demonstrate self-sensing absorbers will work better than the former but a little worse than the latter .

關鍵字(中)

★ 壓電吸振器
★ 自感式

關鍵字(英)

★ piezoelectric absorber
★ self-sensing

論文目次

目錄..........................................................................I
圖索引.......................................................................IV
表索引......................................................................VII
符號說明...................................................................VIII
第一章序論...................................................................1
1.1前言.......................................................................1
1.2文獻回顧...................................................................1
1.3 內容摘要..................................................................2
第二章系統之運動方程式.......................................................3
2.1壓電材料之介紹.............................................................3
2.1.1壓電材料之基礎理論.......................................................3
2.1.2 壓電方程式..............................................................4
2.2 系統之運動方程式..........................................................6
2.2.1 基本假設................................................................6
2.2.2 運動方程式之推導........................................................7
2.3運動方程式簡化............................................................11
第三章壓電吸振器之電路方程式................................................14
3.1被動式壓電吸振器..........................................................14
3.2主動式之速度回饋壓電吸振器................................................16
3.3主動式之位移回饋壓電吸振器................................................18
3.4自感式壓電吸振器..........................................................19
3.4.1壓電感測器之設計........................................................20
3.4.2.自感式壓電吸振器.......................................................23
3.5 系統近似解...............................................................24
第四章數值結果與分析........................................................26
4.1 系統參數設定.............................................................26
4.2 壓電感測器...............................................................26
4.3 自感式壓電吸振器.........................................................29
4.3.1 吸振器與薄板耦合之最佳位置.............................................29
4.3.2 吸振器之選擇...........................................................30
4.3.3 阻尼比對吸振器減振之影響...............................................33
4.3.4 吸振器頻率之選擇.......................................................34
4.3.5 壓電材料面積之影響.....................................................35
4.3.6 壓電材料之電容誤差.....................................................37
4.3.7 壓電材料之遲滯效應.....................................................39
4.4.8 應用不同控制方法之減振效果比較.........................................39
第五章結論與建議............................................................42
5.1 結論.....................................................................42
5.2 建議.....................................................................43
參考文獻.....................45

參考文獻

吳朗, 1994, 電子陶瓷-壓電, 全欣科技出版社, 台北市.
許清秀, 2003, 電壓回饋壓電吸振器對平板之振動控制, 國立中央大學機械工程研究所碩士論文, 桃園縣.
Anderson, E. H. and Hagood, N. W., 1994,“Simultaneous Piezoelectric Sensing/ Actuator：Analysis And Application To Controlled Structures,”Journal of Sound and Vibration, Vol. 174, pp. 617-639.
Bailey, T., and Hubbard, J. E., 1985,“Distributed Piezoelectric Polymer Active Vibration Control of a Cantilever Beam,”Journal of Guidance, Control, and Dynamics, Vol. 8, No. 5, pp. 605-611.
Dally, J. W. and Riley, W. F., 1991, Experimental Stress Analysis, McGraw-Hill, New York, U.S.A.
Dosch, J. J., and Inman, D. J., and Garcia, E., 1992, “A self-Sensing Piezoelectric Actuator for Collocated Control,”Journal of Intelligent Material Systems and Structures, Vol. 3, pp 166-185.
Hagood, N. W., and von Flotow, A., 1991,“Damping of Structure Vibration with Piezoelectric Materials and Passive Electrical Networks,”Journal of Sound and Vibration, Vol. 146(2), pp. 243-268.
Hollkamp, J. J., 1994,“Multimodal Passive Vibration Suppression with Piezoelectric Materials and Resonant Shunts,”Journal of Intelligent Material Systems and Structure, Vol. 5, pp. 49-57.
Nye, J. F., 1964, Physical Properties of Crystals, Oxford, Clarendon Press.
Park, C. H. and Inman, D. J., 2003,“Enhanced Piezoelectric Shunt Design,”Shock and Vibration, Vol.10, pp. 127-133.
Tiersten, H. F., 1969, Linear Piezoelectric Plate Vibration, Plenum, New York,U.S.A.
Vinson, J. R., 1988, The Behavior of Thin Walled Structures, Kluwer Academic Publishers, The Netherlands.
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.

指導教授

黃以玫(Yii-Mei Huang)

審核日期

2004-7-8

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