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研究生: 呂祈曄
Lyu, Chi-Ye
論文名稱: 貼附有壓電片之多跨距Timoshenko曲樑承受移動負載之動態分析
Dynamics Analysis of Moving Load on Multi-span Timoshenko Curved Beam Surface-Mounted with Piezoelectric Layer
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: 2017
畢業學年度: 105
語文別: 中文
論文頁數: 87
中文關鍵詞: 振動曲樑壓電材料移動負載多跨距
外文關鍵詞: Curved beam, Timoshenko beam, Piezoelectric, modal analysis, moving load, electric charge
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  • 本文探討一個貼附有壓電材料多跨距Timoshenko簡支撐曲樑之動態響應,整體結構上層為鋁樑,並在鋁樑下方貼附有壓電材料,每個跨距的弧度皆為 (=1rad)。利用模態法計算出整體結構之自然振動頻率,並探討結構受移動負載之動態響應。
    為了解壓電曲樑運動行為,利用應力場、應變場、位移場推導出應變能和動能,並與外力所作之功結合Hamilton’s Principle求得壓電曲樑之運動方程式與邊界條件,再將運動方程式中之雙變數函數拆成時間與角度兩個單變數函數,配合邊界條件,計算出自然振動頻率和對應之模態示意圖,並討論不同參數的影響。
    應用模態法分析結果為基礎,在壓電曲樑上施加一移動負載,並利用Runge-Kutta數值分析求解動態方程式,同時計算壓電曲樑之位移大小與壓電片所收集之電荷量,改變壓電片幾何條件…等參數,並施加電阻,探討位移及電荷量變化之情形。

    The purpose of this thesis is to explore the dynamic analysis of the Multi-span Timoshenko curved beam with a piezoelectric layer fully mounted below. The governing equations and boundary conditions of the entire beam are derived via the Hamilton’s principle. The natural frequencies and the corresponding sets of mode shape functions are obtained by analytical method. The method of modal analysis is adopted to investigate the dynamic responses of the structure and the electric charge accumulated on the surfaces of the piezoelectric segment caused by a moving load. The effects of traveling velocity of the load and the geometric parameters of the piezoelectric layer on both histories of the displacement of the host beam and the electric charge accumulation on the piezoelectric surfaces are investigated.
    There is a critical velocity of the traveling load to cause the absolute maximum deflection of the host beam. Furthermore, there is another critical velocity of the traveling load to induce the absolute maximum electric charge on the surfaces of the piezoelectric segment. A resistor is implemented to connect the top surface and the bottom surface of the piezoelectric layer to suppress the vibration of the beam. Moreover, the effect of span number on histories of the displacement of the structure and the electric charge accumulation on the piezoelectric surfaces also are investigated.

    目錄 摘要 II Extended Abstract III 致謝 IX 目錄 X 表目錄 XIII 圖目錄 XIV 符號說明 XVIII 第一章緒論 1 1-1前言 1 1-2文獻探討 3 1-3壓電材料(piezo electrics) 5 1-4論文架構 7 1-5基本假設 8 第二章 研究方法與內容 9 2-1運動方程式 9 2-1-1研究模型設定 9 2-1-2位移函數 10 2-1-3壓電材料應力、應變、應變能、動能 12 2-1-4樑之應力、應變、應變能、動能 15 2-1-5 結構運動方程式與邊界條件 17 2-2模態法分析 21 2-2-1改寫運動方程式 21 2-2-2自然振動頻率 23 2-3強迫振動 29 2-3-1移動負載之振動響應方程式 29 2-3-2Rung-Kutta法解移動負載方程式 32 第三章案例探討與數據分析 34 3-1材料參數 34 3-2自然振動頻率 35 3-3位移模態圖 40 3-4整體結構受移動負載之動態分析 41 3-4-1移動負載速度對最大位移點之變化 42 3-4-2改變移動負載速度對電荷收集的變化 46 3-4-3改變移動負載速度對電壓的變化 48 3-4-4改變壓電片厚度對最大位移處之位移歷程變化 50 3-4-5改變壓電片厚度對電荷收集的變化 52 3-4-6改變壓電片厚度對電壓的變化 54 3-4-7改變鋁樑厚度對最大位移處之位移歷程變化 56 3-4-8改變鋁樑厚度對電荷收集的變化 58 3-4-9改變鋁樑厚度對電壓的變化 60 3-4-10改變整體結構半徑對最大位移處之位移歷程變化 62 3-4-11改變整體結構半徑對電荷收集的變化 64 3-4-12改變整體結構半徑對電壓的變化 66 3-4-13多跨距比較 68 第四章結論與建議 81 4-1結論 81 4-1-1自然振動頻率分析 81 4-1-2動態分析 81 4-1-3多跨距分析 81 4-2建議 82 參考文獻 83 附錄A 85 附錄B 87

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