壓電陶瓷平板、薄殼、與雙晶片三維耦合動態特性之實驗量測、數值計算與理論解析

Experimental Measurement, Numerical Calculation and Theoretical Analysis on Three-Dimensional and Coupled Vibration Characteristics of Piezoceramic Plates, Shells, and Bimorphs

黃育熙(Yu-Hsi Huang)

指導教授 ： 馬劍清

國立臺灣大學/工學院/機械工程學研究所/博士(2009年)

https://doi.org/10.6342/NTU.2009.00285

摘要

本文對壓電材料的三維動態特性進行完整的研究與分析，包含單層的壓電陶瓷平板，具有曲率的壓電陶瓷薄殼，以及使用多層組合以增強結構並可達到更大位移效果的壓電雙晶片。文中利用實驗量測、數值計算、與理論解析的方法對各式壓電材料的三維動態特性進行研究，並提出評估壓電材料振動效率的電極設計方法。研究以實驗量測不同電極設計的壓電平板與薄殼的三維振動特性，並對應理論解析與有限元素分析結果，而經電極設計與含裂紋的壓電平板於高頻面內振動時的全域溫度分佈，本論文亦進行實驗量測與數值計算的研究；多層壓電雙晶片的研究中利用串聯與並聯的電位給定模式的變化，對不同極化特性的壓電雙晶片進行三維振動特性的分析，深入的瞭解各種壓電材料的動態特性。
壓電材料的實驗量測則使用多種方法進行分析，全域式的電子斑點干涉術可同時針對壓電材料的面內與面外的模態振形與共振頻率進行量測，並記錄激振電壓可作為三維振動效率的參考依據；雷射都卜勒振動儀可應用動態系統對壓電材料單點的面外振動進行穩態掃頻量測，並利用脈衝訊號激發的暫態量測訊號進行時頻轉換，兩種方式皆可獲得壓電材料的面外共振頻率；阻抗分析儀則以壓電材料的電性量測並可對應面內振動的共振頻率，同時亦可獲得反共振頻率的量測，再經由計算得到機電耦合係數，作為壓電材料於各模態的動態效率指標；紅外線熱像儀可即時且全域的量測壓電材料的溫度分佈。理論解析則採用疊加法以四種對稱位移形式分析壓電平板的面內振動特性，並對應實驗的四種電極分佈形式，亦解析了壓電雙層圓盤的軸向、徑向與切向振動特性，獲得不同極化形式壓電雙層圓盤的三維共振頻率。所有實驗量測與理論解析結果皆與有限元素數值計算進行比較，不只在共振頻率與振動模態可互相對應，正規化位移量比較理論解析與實驗量測皆與壓電材料於各方向振動之強度相符，更提出有限元素計算之電通量與理論解析之應力和相互對應，可作為電極設計與模態效率的指標。本研究成果呈現各種壓電材料的三維動態特性於實驗量測、數值計算、與理論解析皆達到相當優異的一致性，本文成果在學術研究領域或工業界的實際應用，提供了壓電材料完整的振動資訊與有效的電極設計方法。

關鍵字

壓電平板 ； 壓電薄殼 ； 壓電雙晶片 ； 共振頻率 ； 振動模態 ； 電極設計 ； 電子斑點干涉術 ； 阻抗分析儀 ； 雷射都卜勒振動儀 ； 紅外線熱像儀 ； 有限元素法 ； 疊加法 ； 三維耦合振動

並列摘要

Three-dimensional and coupled dynamic characteristics of piezoelectric materials are studied in this disertation. The piezoelectric materials, which are including piezoceramic plate, shell, piezoelectric two-layer discs and rectangular bimorphs, are used experimental measurements, finite element method (FEM), and theoretical analyses to study the out-of-plane and in-plane vibration characteristics. Electrode design method is proposed to enhance the vibration mode efficiency for piezoelectric materials, and is applied to piezoelectric plate and shell in experimental measurement. The experimental results of vibration characteristics are verified with theoretical analysis and numerical calculation. Temperature field is also studied for the piezoceramic plate with segmented electrodes and with crack when the specimens vibrate at high frequency. Furthermore, multilayer piezoelectric component is composited of the same and opposite poling direction, and it has different vibration characteristics by series and parallel electrically connection. This investigation thoroughly understands three-dimentsional dynamic characteriscs of several piezoelectric materials by experimental measurements, numerical calculations, and theoretical analyses.
Several experimental techniques are used to measure the dynamic characteristics of piezoelectric materials in this study. First, the full-filed optical technique, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), can measure simultaneously the resonant frequencies and mode shapes for in-plane and out-of-plane vibration. The excited voltages for mode shapes refer to the efficiency of three-dimensional vibration. Second, the point-wisely measurement system, laser Doppler vibrometer (LDV), can obtain resonant frequencies not only by dynamic signal swept-sine analysis, but also by the time-frequency transform from impulse signal excitation to the piezoceramic plates. Third, the correspondent in-plane resonant frequencies and anti-resonant frequencies are obtained by impedance analysis, and the electromechanical coupling coefficients can be calculated to perform the efficiency of resonance modes. Forth, infrared thermography is also full-field optical technique to measure the distribution of temperature filed. In theoretical analysis, the resonant frequencies, vibration displacements, and stress fileds of piezoceramic plate are derived by superposition method and its symmetric displacement properties of in-plane vibration are corresponding to the four kinds of electrode design in experiment. The transverse, extensional, and tangential vibration characteristics for piezoelectric two-layer discs of the parallel- and series-type polarization are also derived by theoretical analysis. All the results of the experimental measurements and theoretical solutions are compared with the FEM results. Besides, the electrode design method is provided by the summation of in-plane stresses in theoretical analysis, and the stress field is also corresponding with the electric flux of thickness direction in FEM. The vibration mode efficiency of piezoceramic plate and shell can be design by the stress and electric flux fields. It is excellent consistence between resonant frequencies, mode shapes, and normalized displacements on the dominant vibration motion by experimental measurements, finite element numerical calculations, and theoretical analyses.

並列關鍵字

piezoelectric plate ； piezoelectric shell ； piezoelectric bimorph ； resonant frequency ； mode shape ； electrode design ； AF-ESPI ； Impedance analyzer ； LDV ； infrared thermograph ； finite element method ； superposition method ； three-dimensional coupling vibration

參考文獻

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