壓電樑的主動阻尼動態行為分析

Dynamic Analysis of the Active Damping of a Piezoelectric Beam

林瑑璜(Juan-Huang Lin)

指導教授 ： 林水木

崑山科技大學/工程學院/機械工程研究所/碩士(2004年)

https://doi.org/10.6828/KSU.2004.00031

摘要

本文研究利用配對的感應器和作動器壓電片作為彈性拘束均勻樑之主動阻尼的振動控制。首先，利用運動平衡方程式，推導出耦合統御微分方程式和邊界條件。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。本文提出一套方法，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解析解，並推導矩陣基本解表示之特徵方程式。進一步，研究壓電片幾何性質、材料性質、控制條件、邊界條件對自由頻率、模態和穩定性的影響。

關鍵字

解析解 ； 穩定性 ； 壓電 ； 主動阻尼 ； 振動 ； 複變數

並列摘要

This paper investigates the active damping vibration control and its stability of a uniform beam with time-dependent elastic boundary conditions, adhered with conjugated sensor and piezoelectric actuator. First the coupled governing equations with their boundary conditions were derived by the Kinetics of a vibrating beam. The characteristics of the Mathematic model and its relationship with the vibrating behaviors were discussed.
Because of the piezoelectric control in the system, the complex variable terms would appear in differential equations. This paper suggested a method, which can transform the differential equations with complex variables into coupled equations by real part and imaginary part. The transformed equations can be expressed by matrix forms. The semi analytical solutions of matrix from the differential equations were derived first, and then the eigenvalue equations of matrix solutions were derived. Furthermore, how the geometric features of piezoelectric actuator, properties of material, conditions of control, and boundary conditions affected the free frequency, mode state, and stability of the system were studied.

並列關鍵字

vibration ； piezoelectric ； analytical solutions ； complex variables ； active damping ； stability

參考文獻

[1] T. Bailey, & J. E. Hubbard Jr, “Distributed piezoelectric-polymer active vibration control of a cantilever beam,” J. Guidance, Vol. 8(5), 1985, 605-611.

[2] H. S. Tzou, G. C. Wan, “Distributed structural dynamics control of flexible manipulators －Ⅰ. Structural dynamics and viscoelastic actuator,” Computrs and Structures, Vol. 35, pp. 669-677, 1990.

[3] C. K. Lee, W. W. Chiang, T. C. O’Sullivan, “Piezoelectric modal sensor/actuator pairs for critical active damping vibration control,” Journal of Acoustic Slciety of America, 90(1991), 374-384.

[5] E. Dimitriadis, C. R. Fuller, C. A. Rogers, “Piezoelectric actuator as elements of intelligent structures,” AIAA Journal, 25(1987), 1373-1385.

[7] E. F. Crawley, J. D. Luis, “Use of piezoelectric actuators as elements of intelligent structures,” AIAA Journal, Vol. 25, NO. 10, 1987, 1373-1385.