壓電圓盤與壓電圓環共振特性的理論分析與實驗量測

Theoretical Analysis and Experimental Measurements on Resonant Characteristics of Piezoceramic Circular and Annular Plates

何祥瑋(Hsiang-Wei Ho)

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(2005年)

https://doi.org/10.6342/NTU.2005.00582

摘要

由於壓電陶瓷圓盤及圓環具有較簡單且對稱之幾何形狀，使其不論在理論分析推導或試片的製造上都較為容易且常見，因此在實際應用上佔有很大的比例。為了增進邊界效應對壓電陶瓷圓盤和圓環在頻率、振型及機電耦合係數影響差異性的瞭解，因此在其共振頻率及共振模態的實驗量測上有其必要性。本文將針對壓電陶瓷圓盤和壓電陶瓷圓環的振動特性進行理論分析，數值計算和實驗研究，以期對壓電元件之振動行為有完整的了解。
本論文首先推導固定邊界壓電陶瓷圓盤，和單邊固定壓電陶瓷圓環的理論分析，在面外彎曲振動理論推導考慮非對稱的振動模態，而面內徑向和切向振動只探討對稱的模態，文中使用光學全域式的振幅變動電子斑點干涉術以及逐點式的雷射都卜勒振動儀和阻抗分析儀等三種實驗量測技術，並配合有限元素分析針對壓電陶瓷圓盤及圓環的振動特性加以分析，以期能對於壓電陶瓷元件更廣泛之應用與更深入的研究分析能有所助益。文中對於力學問題的振動頻率和模態以及電學問題的電流及機電耦合係數皆有深入且詳細的探討。

關鍵字

壓電陶瓷 ； 共振頻率 ； 共振模態 ； 機電耦合係數

並列摘要

The piezoceramic circular and annular plates have simple and symmetrical geometrical shapes. Therefore, it is easy for theoretical analysis and the manufacturing of specimen. These piezoceramic devices have many industrial applications. To have a thoroughly understanding of frequencies, mode shape and electromechanical coupling coefficient for piezoceramic circular and annular plates, the experimental measurement of resonant frequencies and mode shapes is needed. This thesis will focus on the theoretical analysis, numerical calculation and experimental measurement of piezoceramic annular plates for resonant frequencies and vibration mode shapes.

This thesis will, at first, analyze theoretically the dynamic characteristics analysis of piezoceramic circular plates with fixed boundary and piezoceramic annular plates with one fixed boundary. In out-of-plane vibration (transverse) analysis, the non-symmetric modes are investigated. In in-plane (extensional and tangential) vibration, only the symmetric modes are considered .In this study, three experimental techniques, including AF-ESPI, LDV, and impedance analyzer, are used to obtain the vibration characteristics of piezoceramic circular and annular plates .The experimental results are compared with the FEM and analytical solutions . The resonant frequency, mode shape,electric current and electromechanical coupling coefficient for out-of-plane and in-plane vibration modes are analyzed and discussed in detail .

並列關鍵字

piezoceramic ； resonant frequencies ； resonant mode shapes ； electromechanical coupling coefficient

參考文獻

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