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博碩士論文 etd-0831104-224324 詳細資訊
Title page for etd-0831104-224324
論文名稱
Title
壓電樑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 Beam
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
109
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
2004-07-23
繳交日期
Date of Submission
2004-08-31
關鍵字
Keywords
壓電參數、最佳化
Optimization, Piezoelectric Parameters
統計
Statistics
本論文已被瀏覽 5740 次,被下載 2986
The thesis/dissertation has been browsed 5740 times, has been downloaded 2986 times.
中文摘要
本論文主要在探討壓電樑自然頻率反算壓電材料參數之可行性。由於一般壓電各項材料參數涉及壓電與應力、應變效應,不多同時測得,一次均以一項參數為量測對象,其餘參數保持一定值,忽略彼此之交互影響效應,故所獲得的壓電參數與實際使用值,會有所差異。本論文以壓電樑的自然頻率為分析對象,配合數值計算與最佳化方法進行相關壓電材料參數之反算。
文中首先利用漢米爾頓原理推導壓電樑運動方程式,並以微分值積法(DQM)求解特徵值問題。之後利用遺傳演算法進行壓電參數值之最佳化,文中將特徵值求解過程併入最佳化流程內,同時就所有壓電參數進行最佳化。文中分別針對邊界為兩端固定與固定-自由端之壓電樑,分別進行材料參數最佳化之研究。除了利用數值範例確認程式強韌性外,並以實驗數據為基準,進行壓電材料參數之最佳化。分析數據與結果顯示利用自然頻率反算材料參數確有其可行性與實用價值。
Abstract
In this thesis, the feasibility of inverse evaluation of piezoelectric parameters by using piezoelectric beam’s natural frequencies is presented. Generally, all the piezoelectric parameters are not measured simultaneously. In other words, the interactive effects between the piezoelectricity and strain are not all included. The piezoelectric beam’s natural frequencies are analyzed by the inverse evaluation of piezoelectric parameters associated with the optimization algorithm.
The dynamic model for piezoelectric beam is proposed by using Hamilton’s principle in this study. The corresponding eigenvalue problems of different piezoelectric beams are formulated and solved by employing differential quadrature method (DQM). The genetic optimization algorithm is employed to optimize all piezoelectric parameters from the measured natural frequencies. Optimization of piezoelectric parameters of piezoelectric beam under the boundary conditions of fix-fix ends and fix-free ends are investigated. The robustness of program is also demonstrated through several numerical examples. The results demonstrate the method of this study applied to determine piezoelectric parameters by using natural frequencies is feasible and practicable.
目次 Table of Contents
目錄 I
圖目錄 IV
表目錄 VII
符號說明 IX
摘要 XII
Abstract XIII
第一章 緒論 1
1-1前言 1
1-1-1 簡介 1
1-1-2 研究動機與目的 2
1-1-3 研究方法 4
1-2文獻回顧 5
1-2-1微分值積法 5
1-2-2 壓電理論 6
1-2-3 遺傳演算法 8
1-3 組織與章節 8
第二章 理論與數值方法 10
2-1 微分值積法 10
2-1-1簡介 10
2-1-2 權係數 11
2-1-3 取樣點 13
2-2 壓電理論 14
2-3遺傳演算法 22
2-3-1簡介 22
2-3-2編碼與解碼 23
2-3-3適存函數 26
2-3-4交配 26
2-3-5突變 27
第三章 DQM解壓電樑之自然頻率 31
3-1 壓電樑運動方程式之推導 31
3-2 壓電樑自然頻率 36
3-3小結 44
第四章 壓電材料參數之最佳化設計 47
4-1數值範例分析 47
4-2與實驗值比對之壓電參數最佳化 76
第五章 結論 101
5-1 結論 101
5-2 未來展望 103
參考文獻 104
參考文獻 References
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