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研究生:邱文元
研究生(外文):Chiu-WenYuan
論文名稱:壓電曲樑承受移動負載之動態響應分析
論文名稱(外文):Dynamic Response of Curved Piezoelectric Beam Subjected to a Moving Load
指導教授:王榮泰
指導教授(外文):Wang-Rong Tai
學位類別:碩士
校院名稱:國立成功大學
系所名稱:工程科學系
學門:工程學門
學類:綜合工程學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:中文
論文頁數:69
中文關鍵詞:壓電曲樑移動負載模態法
外文關鍵詞:Curved piezoelectric beamMoving loadModel analysis method
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本文探討貼附有壓電片Timoshenko曲樑之動態分析,將壓電材料貼附在整體結構的第二跨距下方,採用模態法計算自然頻率變化並探討此結構受移動負載之動態響應及電荷收集的情形。
利用應力場和應變場推導出此壓電曲樑之應變能項與動能項,再以漢米爾頓原理得出結構樑之運動方程式。
模態法則是將運動方程式中的雙變數函數拆成兩個單變數函數求解出位移函數,配合邊界條件計算出力場函數,進而求解結構自然頻率,並討論在不同的幾何參數下對模態頻率的影響。
動態分析則是以模態法作為基礎,施加一個移動負載,探討改變結構及壓電片幾何條件對整體樑的自由端位移變化以及壓電片收集電荷情形。

The purpose of this thesis is to study the dynamic responses of a curved beam,which has a piezoelectric sheet mounted on the bottom surface. The Timoshenko theory is adopted in this study. The lower layer of the second span is a piezoelectric sheet. The displacement and rotation of all components of the entire beam are set. The displacements, stresses, strains, electric field and electric displacements are used to derive strain energy, kinetic energy. The governing equations and the corresponding boundary condition are derived via the Hamilton’s principle. The natural frequencies are obtained by analytical method. Dynamic analysis is based on the modal analysis method. The method is presented to obtain the dynamic responses of the entire beam induced by a load moving on the beam. The effects of traveling velocity of the load and the geometric parameters of the beam on both histories of the displacement of the beam and the electric charge accumulation on the piezoelectric surfaces are investigated.
摘要 I
Extended Abstract II
誌謝 VII
目錄 VIII
表目錄 XII
圖目錄 XIV
符號說明 XV
第一章 緒論 1
1-1 研究動機 1
1-2文獻探討 2
1-3 論文架構 6
1-4 研究架構流程 7
1-5 本文基本假設 8
第二章 壓電曲樑之運動方程式推導 9
2-1模型設定 9
2-2 應變能與動能 10
2-3壓電理論 12
2-4 Hamilton’s principle 16
2-5各跨距之邊界條件 19
第三章 模態法 20
3-1 第一和第三跨距之位移場及合應力場推導 20
3-2 第二跨距之位移場及合應力場推導 22
3-3 代入各跨距位移場及合應力場 27
3-4利用邊界條件計算自然頻率 28
第四章 移動負載之振動分析 29
4-1推導承受移動負載之振動響應方程式 29
4-2 動態模擬方程式 32
第五章 案例探討與數據分析 34
5-1案例探討 34
5-1-1 材料幾何條件 34
5-2 自然振動頻率數據討論 35
5-2-1 整體樑之自然頻率與模態圖 35
5-2-2改變不同曲樑半徑對自然頻率影響 37
5-2-3改變壓電片厚度對自然頻率影響 39
5-2-4改變壓電片長度對自然頻率影響 40
5-2-5改變壓電片位置對自然頻率影響 41
5-3整體樑結構受移動負載速度之動態分析 42
5-3-1改變移動負載速度對自由端位移的變化 43
5-3-2 速度比對結構自由端位移極值之比較 44
5-3-3改變移動負載速度對電荷量收集的變化 45
5-3-4速度比對壓電片收集電荷量極值之比較 46
5-3-5同速度下改變曲樑半徑對自由端位移極值及電荷極值比較 47
5-3-6同速度下改變壓電片厚度對自由端位移極值及電荷極值比較 48
5-3-7同速度下改變壓電片長度對自由端位移極值及電荷極值比較 49
5-3-8同速度下改變壓電片位置對自由端位移極值及電荷極值比較 50
5-3-9改變曲樑半徑對於臨界速度比與自由端位移極值之比較 51
5-3-10改變壓電片厚度於臨界速度比與自由端位移極值之比較 52
5-3-11改變壓電片長度於臨界速度比與自由端位移極值之比較 53
5-3-12改變壓電片位置於臨界速度比與自由端位移極值之比較 54
5-3-13改變曲樑半徑對臨界速度比與電荷量極值之比較 55
5-3-14改變壓電片厚度對臨界速度比與電荷量極值之比較 56
5-3-15改變壓電片長度對臨界速度比與電荷量極值之比較 57
5-3-16改變壓電片位置對臨界速度比與電荷量極值之比較 58
第六章 結論與建議 59
6-1自然振動頻率分析 59
6-2 固定移動負載速度之動態分析 60
6-3 臨界移動負載速度之動態分析 61
6-4建議 62
參考文獻 63
附錄A 68
附錄B 69


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