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研究生：	江宗駿 Jiang, Zong-Jyun
論文名稱：	貼附有壓電片之多跨距Timoshenko樑承受移動負載之動態分析 Dynamics Analysis of Moving Load on Multi-span Timoshenko 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：	133
中文關鍵詞：	多跨距之簡支樑、壓電片、模態法、移動附載
外文關鍵詞：	Multi-span Timoshenko beam, Piezoelectric, modal analysis, moving load, electric charge
相關次數：	點閱：66 下載：0
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本文目的為探討一根多跨距且單邊貼附有壓電片之Timoshenko簡支樑承受移動負載之震動分析且採用模態法來分析此多跨距樑之動態響應。
模態法方面，為了解此根多跨距的壓電簡支撐樑之力學行為，需利用應力場、應變場及結構位移關係於求出應變能、動能，再以Hamilton’s principle建立此多跨距的壓電樑之統御方程式。統御方程式則可利用於求取結構之模態頻率與模態形狀函數，並探討多跨距結構之不同結構設定對於模態頻率之影響。
模態法中關鍵之模態形狀函數及模態頻率求得後，可運用模態形狀函數推導出結構承受移動負載之動態方程式，接著使用模態疊加法及Runge-Kutta 數值分析法求解結構承受移動負載之動態響應，進而探討結構之響應、壓電片之電荷收集情形、壓電片之壓電感應電壓，了解多跨距結構對於響應、電荷收集情形、壓電感應電壓之影響。

The purpose of this thesis is to explore the dynamic analysis of the multi-span Timoshenko beam with a piezoelectric segment surfaced-mounted on each span. 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 moving load. The effects of moving 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 moving load to cause the absolute maximum deflection of the host beam. Furthermore, there is another critical velocity of the moving load to induce make the absolute maximum electric charge on the surfaces of the piezoelectric segment. As the number of span is increased, the maximum displacement at w-history at the mid-point of the first span of the simply-supported multi-span beam is reduced.

摘要	I
Extended Abstract	II
誌謝	VII
目錄	VIII
圖目錄	XI
表目錄	XIV
符號說明	XVI
第一章 緒論	1
1-1研究動機及目的	1
1-2文獻探討	4
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 研究方法及內容	10
2-1研究基本介紹	10
2-1-1研究模型設定	10
2-1-2壓電片PZT-5H	11
2-1-3位移函數	12
2-1-4壓電片本質方程式	13
2-2結構之位移、轉角、應變、應力、受力、能量	15
2-2-1主樑(鋁樑)之位移、轉角、應變、應力、受力、能量	15
2-2-2壓電片之位移、轉角、電位移、應變、應力、受力、能量	16
2-2-3鋁樑貼附有壓電片部分	18
2-3 利用Hamilton’s principle求結構運動方程式與邊界條件	19
2-3-1Hamilton’s principle	19
2-3-2變分法	19
2-3-4結構運動方程式(Governing Equations)	22
2-3-5邊界條件(Boundary Conditions)	24
2-4自由震動	26
2-4-1雙變數函數轉單變數函數	26
2-4-2位移函數與合力場函數以矩陣表示	27
2-4-3模態常數個數一致化	29
2-4-4位移場與應力場	30
2-4-5自然振動頻率	32
2-5強迫震動	35
2-5-1運動方程式之建立	35
2-5-2 Runge-Kutta Method解運動方程式	37
第三章 案例探討與模擬數據	39
3-1參數設定	39
3-2案例分析	40
3-2-1具三跨距結構之結果	40
3-2-3多跨距比較─跨距數量	81
第四章 結論與建議	105
4-1結論	105
4-1-1一個三跨距結構分析	105
4-1-2跨距幾何設定相同之多跨距結構分析	106
4-2建議	108
參考文獻	109
附錄	111
                                    

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[15] 曾紹齊, “單邊貼附有壓電材料之Timoshenko樑承受移動負載之動態分析,” 成功大學工程科學系碩士論文, 2016.

校內：2022-07-01公開
校外：不公開電子論文尚未授權公開，紙本請查館藏目錄

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