壓電矩形板動態特性之理論分析及電極設計之影響研究

Theoretical Analysis of Dynamic Characteristics and Investigation of Electrode Design for Piezoelectric Rectangular Plates

郭椿億(Chun-Yi Kuo)

指導教授 ： 馬劍清

國立臺灣大學/工學院/機械工程學研究所/碩士(2008年)

https://doi.org/10.6342/NTU.2008.02758

摘要

本文主要以理論探討 PZT壓電平板共振時的振頻與振形之動態特性，首先應用變分法推導壓電平板本構方程式與運動方程式，並以疊加法導出面內位移與面內應力的級數解，最後以理論解析為礎來探討壓電平板在自由邊界下的共振頻率與共振模態。將共振頻率與共振模態與有限元素軟體數值計算結果作比較，而兩種數值結果再與阻抗分析儀及振幅變動式電子斑點干涉術兩種實驗量測結果相互驗證。本文有別於以往對於壓電材料的研究大部份只著重於理論分析或是實驗量測探討，很少將兩種結合起來，使得壓電元件的研發設計不僅耗時且增加成本，因此研究壓電元件的動態行為及其溫度效應，可設計及分析壓電元件的特性。接著利用理論計算正向應力和分佈場與有限元素軟體計算得到的電通量進一步設計不同的電極切割，以改善壓電平板不易激振的共振頻率及模態。最後結合紅外線熱像儀量測壓電平板全場的溫度分佈變化情形，探討影響溫度分佈與溫升的歷程。

關鍵字

壓電平板 ； 變分法 ； 疊加法 ； 有限元素法 ； 共振頻率 ； 模態 ； 電極設計 ； 電子斑點干涉術 ； 阻抗分析儀 ； 紅外線熱像儀

並列摘要

The dynamic characteristics, resonant frequencies and mode shapes, of a piezoelectric rectangular plate are analyzed in this thesis. The variation method is used to establish constitutive equations and equations of motion for in-plane vibrations. The analytical solutions for in-plane displacement fields with free boundary and the associated normal stresses are obtained in Fourier’s series. The analytical series solutions are compared with three methods. One is the numerical computation from the of finite element method (FEM) software, another is the impedance spectrum measured by impedance analyzer, and the other is amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) technique. From combination of the results obtained from theoretical prediction and experimental measurement, the dynamic characteristics of piezoelectric plate in resonance are completely analyzed. Furthermore, this thesis also provides the electrode design, according to the sum of the in-plane normal stress distribution and the electric flux calculated by FEM, to improve the excitation of the piezoelectric plate for in-plane vibration. Finally, the temperature distributions of PZT plate excited at different resonant frequency are obtained by infrared thermograph to indicate the influence on temperature field.

並列關鍵字

piezoelectric rectangular plate ； variation method ； superposition method ； resonant frequency ； mode shape ； electrode design ； ESPI ； Impedance analyzer ； infrared thermograph

參考文獻

黃智麟，力學與電學耦合問題之含裂縫壓電陶瓷板動態特性研究與實驗量測，國立台灣大學機械工程研究所碩士論文，94年6月。

Bobnar, V., Kutnjak, Z. and Levstik, A.,“Temperature Dependence of Material Constants of PLZT Ceramics,”Journal of the European Ceramic Society, 19, 1281-1284, (1999).

Boxiang, L., Harald, A., Heiner, E. and Eckhardt, Z.,“Real Time Investigation of Rotating Objects Using ESPI System,” Proceedings of SPIE, 1026, 218-221, (1988).

Butters, J. N. and Leendertz, J. A.,“Speckle Pattern and Holographic Techniques in Engineering Metrology,” Optics and Laser Technology, 3(1), 26-30, (1971).

Cao, W., Zhu, S. and Jiang, B.,“Analysis of Shear Modes in a Piezoelectric Vibrator,” Journal of Applied Physics, 83, 4415-4420, (1998).