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研究生： 周裕捷
Chou, Yu-Chieh
論文名稱： 具有嵌入壓電材料之板振動分析
Vibration Analysis of Mindlin Sandwich Plate with Embedded Piezoelectric Structure
指導教授： 王榮泰
Wang, Rong-Tyai
學位類別： 碩士
Master
系所名稱： 工學院 - 工程科學系
Department of Engineering Science
論文出版年： 2007
畢業學年度： 95
語文別： 中文
論文頁數： 99
中文關鍵詞： 板 、有限元素 、頻率 、壓電
外文關鍵詞： piezoelectric, finite element, plate, frequencies
相關次數： 點閱：64  下載：2 
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    • 本文主要利用有限元素法分析具有嵌入壓電材料之Mindlin板結構的自由振動特性。本文運用Mindlin板理論定義位移、應變與應力，計算出壓電三明治板的應變能及動能，由漢米爾頓原理求得壓電三明治Mindlin板的靜態平衡方程式，使用靜態的運動方程式推導出其位移場之解並表示成形狀函數(shape function)形式。由應變能及位能找出質量矩陣及剛性矩陣，進而利用Lagrange’s equation將應變能及動能代入得到壓電三明治板元素的運動方程式，再依不同的邊界條件將元素結合，解出系統的模態頻率，並與解析解做對照。最後加上電壓，結合有限元素分析結構之位移變形量。再利用回授控制設計於抑制此結構的振動。

    This study presents natural frequencies and vibration control of rectangular plate embedded with piezoelectric material by Finite Element Method.
    Based on Mindlin’s plate theory, the displacements, strains and stresses of plate can be defined to calculate strain energy and kinetic energy. The governing equation are formulated via the Hamilton’s principle. The displacements solved from static equilibrium equations are used as shape functions of one element. The natural frequencies obtained by the finite element method are compared with those analytic results.
    The effect of constant voltage on the deflection of the plate is demonstrated. Further, the vibration suppression of plate with the piezoelectric layers is displayed .

    目錄 摘 要...........................................................................................................1 Abstract.................................................................................................... II 致謝..........................................................................................................III 目錄.......................................................................................................... IV 圖目錄...................................................................................................... VI 表目錄...................................................................................................VIII 第一章 緒論...............................................................................................1 §1-1 前言...........................................................................................1 §1-2 文獻回顧...................................................................................4 §1-3 研究範圍...................................................................................6 第二章 壓電三明治板之運動方程式......................................................8 §2-1 壓電三明治板之應力與應變...................................................8 §2-2 壓電三明治板之電焓與動能.................................................12 第三章 壓電三明治板之振動分析........................................................22 §3-1 壓電三明治板位移場解..........................................................22 §3-2 壓電板通解的矩陣形式及其shape function ..........................28 §3-3 壓電三明治板元素的質量矩陣及剛性矩陣..........................29 §3-4 有限元素用於壓電三明治板之振動分析..............................30 第四章 嵌入式壓電複合層板之振動分析............................................43 §4-1 三明治板之應力與應變..........................................................43 §4-2 三明治板之應變能與動能.....................................................44 §4-3 三明治板之運動方程式.........................................................47 §4-4 三明治板位移場解與本構方程式..........................................52 §4-5 嵌入式壓電複合層板本構方程式..........................................54 第五章 嵌入式壓電複合層板之回授控制............................................58 §5-1 回授控制分析..........................................................................58 §5-2 Newmark’s Scheme..................................................................60 §5-3 問題與討論.............................................................................61 第六章 總結及建議................................................................................68 §6-1 結論.........................................................................................68 §6-2 建議.........................................................................................68 附錄A........................................................................................................70 附錄B........................................................................................................71 附錄C........................................................................................................72 附錄D........................................................................................................74 附錄E........................................................................................................80 附錄F........................................................................................................85 參考文獻...................................................................................................86

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