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研究生: 吳豐羽
Wu, Fong-Yu
論文名稱: 貼附有壓電片之Timoshenko曲樑承受移動負載之動態響應分析
Dynamic Responses of Timoshenko Curved Beam Surface Mounted with Piezoelectric Segment due to Moving Load
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: 2016
畢業學年度: 105
語文別: 中文
論文頁數: 62
中文關鍵詞: 壓電曲樑移動負載模態法抑制震動
外文關鍵詞: Curved beam, Piezoelectric segment, modal analysis, traveling load, electric charge, decay rate
相關次數: 點閱:113下載:5
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  • 本文探討一根貼附有壓電片之Timoshenko曲樑的動態分析;此結構中的第一和第三跨距為Timoshenko樑,第二跨距為壓電複合層曲樑所組成,並使用模態法計算出此結構之模態頻率,進而探討承受移動負載之動態響應。
    而為了要瞭解壓電曲樑之力學行為,利用位移場、應力場與應變場的關係推導出此曲形樑之運動方程式,並以解析的方法於求解此結構之模態頻率與其所對應的模態形狀函數,證明相異的模態頻率其所對應的兩組模態函數具有正交性。並討論在不同的幾何參數下對模態頻率的影響。
    接著應用模態法於分析曲形樑承受一個移動負載,探討施加一個移動負載對於曲形樑之動態響應特性的影響,並使用Runge-Kutta數值分析法求解動態方程式,計算樑之位移大小和壓電片表面的儲存電荷量。改變壓電片的幾何條件、並施加電阻,探討整體樑的自由端所產生的位移變化以及壓電片收集電荷情形。

    The purpose of this thesis is to explore the dynamic analysis of the Timoshenko curved beam with a piezoelectric segment 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 host beam and the electric charge accumulated on the surfaces of the piezoelectric segment caused by a traveling load. The effects of traveling velocity of the load and the geometric parameters of the piezoelectric segment 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 make 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 segment to suppress the vibration of the beam. The effects of the geometric parameters of the piezoelectric segment on the decay rate of vibration will also be investigated.

    摘要----II Extended Abstract----III 誌謝----VIII 目錄---- IX 圖目錄----XII 表目錄----XIII 符號說明----XV 第一章 緒論----1 1-1 研究動機----1 1-2文獻探討----3 1-3 論文架構----7 1-4 研究架構流程----8 1-5 本文基本假設----9 第二章 壓電曲樑之運動方程式推導---- 10 2-1模型設定----10 2-2 應變能與動能----11 2-3壓電理論----13 2-4 Hamilton’s principle----17 2-5各跨距之邊界條件----20 第三章 模態法---- 21 3-1 第一跨距樑與第三跨距樑的位移場及合應力場----21 3-2 第二跨距之位移場及合應力場----23 3-3 代入各跨距位移場及應力場----28 3-4利用邊界條件計算自然振動頻率---- 29 第四章 移動負載之振動分析----30 4-1推導承受移動負載之振動響應方程式----30 第五章 案例探討與數據分析----33 5-1案例探討----33 5-1-1 材料幾何條件----33 5-2 自然振動頻率數據討論----34 5-2-1 整體樑之自然頻率與模態示意圖----34 5-2-2改變壓電片厚度對自然頻率影響----35 5-2-3改變壓電片長度對自然頻率影響----36 5-2-4改變壓電片位置對自然頻率影響----37 5-3簡支曲樑承受移動負載之動態分析----38 5-3-1移動負載速度對最大位移點之變化 ----39 5-3-2臨界速度時簡支曲樑位移極值之比較----42 5-3-3改變移動負載速度對電荷量收集的變化----45 5-3-4臨界速度時壓電片收集電荷極值之比較----47 5-4曲形樑承受移動負載並施加電阻之動態分析----50 5-4-1電阻對於最大位移與電荷量收集的影響----51 5-4-2改變幾何參數之分析----52 第六章 結論與建議----56 6-1自然振動頻率分析----56 6-2壓電片的動態響應----56 6-3曲形樑承受移動負載並施加電阻之動態分析----57 6-4建議----58 參考文獻----59

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