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博碩士論文 etd-0719110-175233 詳細資訊
Title page for etd-0719110-175233
論文名稱
Title
壓電圓盤自然頻率值用於壓電材料參數之擷取
Determination of Piezoelectric Parameters from Measured Natural Frequencies of a Piezoelectric Circular Plate
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
128
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2010-07-03
繳交日期
Date of Submission
2010-07-19
關鍵字
Keywords
振動、壓電材料、壓電常數、介電常數、遺傳演算法、彈性常數、壓電圓盤
piezoelectric constants, genetic algorithm, piezoelectric material, vibration, elastic constants, piezoelectric circular plate, dielectric constants
統計
Statistics
本論文已被瀏覽 5765 次,被下載 4709
The thesis/dissertation has been browsed 5765 times, has been downloaded 4709 times.
中文摘要
由於壓電材料具有電-彈耦合特性,其中多項材料參數,將涉及應力、應變、電位移與電場之交互影響。因其複雜度,在各參數量測時,均無法採用多參數同時測得。目前各參數之測定均須忽略彈性、介電與壓電損失之交互效應,一次以單一參數為量測對象,假設其餘參數保持定值,不致因測定參數之變化而有所變異,因此假設沒有其一定之不確定性,各規範所得材料參數,可能與實際使用值會有所差異。故本論文提出利用壓電圓盤自然頻率搭配遺傳演算法,同時考慮電-彈交互影響,並一次性擷取交互影響較複雜之相關彈性、介電與壓電常數。
文中以特定尺寸之圓形壓電陶瓷板為例,首先針對能含蓋大部分壓電參數之圓盤面外非軸對稱軸向與面內軸對稱徑向振動模態參數加以分析。以理論推導自由邊界壓電圓盤其材料參數與自然頻率之相互關係,由遺傳演算法之最佳化模式,配合不同實驗測得之自然頻率值,透過最佳化程序,同時對大部分壓電材料參數進行最佳化擷取。最後分別利用理論分析模式與有限元素模擬,將文中所提最佳化程序擷取之參數,代入不同邊界條件與不同幾何形狀之壓電板,解得其對應之自然頻率分佈並與實驗測得值進行驗證。結果顯示,經文中所提考慮電-彈交互影響,並一次性擷取之材料參數值,與實驗測試值有較佳之符合度,亦間接證明本文所提之壓電參數測定法之適用性。
Abstract
Due to the complexity of electro-elastic coupling characteristics in piezoelectric material, some of the elastic, dielectric and piezoelectric parameters are difficult to be measured. Usually, these parameters are determined by assuming that all offer parameters are remained constant during the measurement. However, the interactive effect between material properties makes this assumption be not always true. In this study, the measured natural frequencies of the specified circular piezoelectric plate are used to extract these parameters simultaneously. In other words, all these parameters are determined with considering the interactive electro-elastic coupling effect.
The analytic model of free-free circular piezoceramic plate was derived and solved to establish the relationship between natural frequencies and its material parameters, to cover most all the parameters, the out-of-plane(non-symmetric transverse) and in-plane(symmetric extensional) modes are considered. The genetic algorithm is employed to determine most all elastic, dielectric and piezoelectric parameters from a least square error between the calculated and measured natural frequencies. Numerical results derived from the parameters proposed in this work reveal a good agreement with the measured data. In other words, the proposed method to extract the piezoelectric parameters is feasible and effective.
目次 Table of Contents
目錄 i
表目錄 iii
圖目錄 iv
符號說明 vii
摘要 xi
Abstract xiii
第一章 緒論 1
1-1 壓電材料簡介 1
1-2 研究動機與目的 3
1-3 文獻回顧 5
1-4 組織與章節 10
第二章 研究理論與數值方法 11
2-1 壓電理論 11
2-2 壓電材料參數轉換與測量 17
2-3 遺傳演算法 20
第三章 壓電材料參數對自然頻率之影響 28
3-1 壓電薄板振動特性理論解析之基本假設 28
3-2 壓電圓盤之理論解析 31
3-2-1 面外振動之自然頻率 33
3-2-2 面內振動之自然頻率 38
3-3 壓電圓環之理論解析 41
3-3-1 面外振動之自然頻率 42
3-3-2 面內振動之自然頻率 48
3-4 壓電元件之有限元素模型 51
第四章 壓電材料參數之擷取 52
4-1 範例材料簡介與實驗數據 52
4-2 擷取流程範例與討論 61
4-3 自然頻率誤差值對參數敏感度分析 76
4-4 擷取參數驗證 86
第五章 結論與未來展望 102
5-1 結論 102
5-2 未來展望 103
參考文獻 105
參考文獻 References
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