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研究生： 張晏徵
Chang, Yen-cheng
論文名稱： 貼附式壓電材料懸臂樑具焦電效應之振動分析
Dynamics of Timoshenko Beam Surface Mounted With Piezoelectric Material Inculding Pyroelectric Effect
指導教授： 王榮泰
Wang, Rong-tai
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： 2008
畢業學年度： 96
語文別： 中文
論文頁數： 110
中文關鍵詞： 有限元素法 、回授控制 、制振 、荷密頓定理 、邊界條件 、壓電材料 、模態法 、Newmark 法 、動態模擬 、Gain 值 、模態頻率 、Lagrange 方程式 、控制方程式
外文關鍵詞： actuator, feedback, gain, sensor, piezoelectric, pyroelectric, finite element, modal frequencies, temperature distribution, vibration suppression
相關次數： 點閱：164  下載：3 
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    • 本文目的為探討貼附式壓電材料懸臂樑之動態響應，而以有限元素法為動態模擬的基底，並以模態法來驗證有限元素法之可行性；再以有限元素方式做回授控制，分析此一結構在回授控制的制振效果。

    此結構中的第一和第三跨距為單層的鋁材，第二跨距為三層的壓電三明治複合層樑，其中上下層為壓電材料、中間層為鋁材所構成。

    我們利用結構的應力、應變場與連續位移條件推出應變能&動能方程式，再以Hamilton’s Principle求得governing equations & boundary conditions。

    在模態法方面，利用governing equations求得壓電層樑之運動方程式，再利用boundary conditions找出各跨距左右端點之關係，進而計算出模態頻率。

    在有限元素法方面，則使用靜態結構方程式推導出其位移場之通解，藉由應變能項與動能項計算出結構的勁度矩陣和質量矩陣，建立出有限元素模型，再利用堆疊方式經Lagrange’s equation 解出系統的模態頻率，並選取不同數目之元素來堆疊此結構，將結果與模態法之結果相較，以此確認有限元素法之可行性。

    在回授控制方面，用有限元素法為基底，再以Newmark’s scheme對此結構進行動態模擬其制振情況。並探討壓電材料之Gain值、位置、長度&厚度效應對於整體結構的制振效果。

    The dynamics of Timoshenko beams surface mounted with piezoelectric materials inculding the pyroelectric effect is studied. The finite element approach is presented. The static responses obtained by the approach is exact the same as those by analytic method. Furthermore, the modal frequencies of the beam obtained by the approach also compare well with those by analytic method.
    One layer of piezoelectric layer acts as a sensor and the other layer acts as an actuator via a feedback system. The effects of gain of the feedback system, and the location, length, thickness and temperature distribution of the piezoelectric materials on the vibration suppression of the beam are investigated.

    摘要 I Abstract II 誌謝 III 目錄 IV 表目錄 VII 圖目錄 VIII 符號說明 XI 第一章 緒論 1 §1-1 前言 1 §1-2 文獻回顧 3 §1-3 論文架構 6 第二章 研究架構 7 §2-1 架構流程 7 §2-2 本文基本假設 8 第三章 研究方法及內容 9 §3-1 運動方程式推導 9 §3-1-1 初始設定 9 §3-1-2 Timoshenko Beam之應力 & 應變 11 §3-1-3 應變能( S ) & 動能( T ) 12 §3-1-4 透過Hamilton’s principle獲得governing equations & boundary conditions 14 §3-1-5 governing equations & boundary conditions 16 §3-2 有限元素法分析 19 §3-2-1 靜態平衡方程式 19 §3-2-2 以矩陣形式表示位移函數 20 §3-2-3 以兩端點表示位移場 21 §3-2-4 單位元素之勁度矩陣 & 質量矩陣 22 §3-2-5 單位元素矩陣堆疊 23 §3-2-6 自然振動頻率 23 §3-3 模態法分析 24 §3-3-1 改寫governing equagotions，使雙變數函數拆為兩單變數函數 24 §3-3-2 以矩陣形式表示位移函數 25 §3-3-3 以矩陣形式表示力場函數 26 §3-3-4 位移場&力場組合以跨距兩端點表示 27 §3-3-5 自然振動頻率 29 §3-4 回授控制分析 30 §3-4-1 感測器(Sensor)輸出之電流 31 §3-4-2 制動器(Actuator)與感測器(Sensor)之作用力 31 §3-4-3 回授阻尼矩陣 32 §3-4-4 Newmark’s scheme 33 第四章 案例探討與模擬數據分析 34 §4-1 案例探討有限元素模型 34 §4-1-1 各參數值 35 §4-1-2 有限元素法和模態法之自然頻率比較 35 §4-1-3 位移模態圖 39 §4-2 案例探討回授控制影響 40 §4-2-1 效應推論 40 §4-2-2 解析解與有限元素之相互印證 42 §4-2-3 壓電片位置對感測器應變之影響 43 §4-2-4 壓電片厚度對感測器應變之影響 44 §4-2-5 比較在不同外力影響下之w位移 (改變壓電片位置) 45 §4-2-6 比較在不同外力影響下之w位移(改變壓電片長度 ) 46 §4-2-7 比較在不同外力影響下之w位移(改變壓電片厚度 ) 47 §4-2-8 Gain值效應 48 §4-2-9 壓電材料之位置效應( 效應) 57 §4-2-10 壓電材料之長度效應( 效應) 66 §4-2-11 壓電材料之厚度效應( 效應) 75 第五章 結論與建議 84 §5-1 結論 84 §5-2 建議 86 參考文獻 87 附錄A 91 附錄B 92 自述 96

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