臺灣博碩士論文加值系統

本文為探討貼附有壓電材料Timoshenko懸臂樑與簡支樑之動態響應，結構中的第一和第三跨距為單層的 Timoshenko 樑，第二跨距為Timoshenko 樑上層貼附有壓電材料所組成，採用模態法計算壓電懸臂樑的自然頻率變化並探討此結構受移動負載之動態響應。
在模態法方面，為了解壓電層樑之力學行為，則利用應力場、 應變場與位移場的關係推導出應變能和動能，再以Hamilton's Principle求得壓電層樑之運動方程式，再將運動方程式中的單變數轉換為時間和距離雙變數，再配合邊界條件計算出力場函數，進而解出模態頻率與模態示意圖，並討論在不同的幾何參數條件下對模態頻率之影響。
動態響應則是以前述的模態法作為基礎，施加一個移動負載並使用Runge-Kutta數值積分法於求解動態方程式，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 study the coupling effects of mechanical and electrical responses of two types of Timoshenko beams: cantilevered and simply-supposed, which is mounted with a piezoelectric material on the top surface.
The charge equation of the piezoelectric material is included in the study. Governing equations and boundary conditions are derived via the Hamilton’s principle. The natural frequencies and the corresponding sets of mode shape functions are obtained by analytical method. A moving load on the beam is taken as an example. 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. In order to suppress the vibration of the beam, a resistor is connected the top surface and the bottom surfaces of piezoelectric material. Runge-Kutta method is adopted to analyze the beam’s kinetic response.

目錄
摘要 I
Extended Abstract II
誌謝 VIII
表目錄 XIV
圖目錄 XVIII
符號說明 XXI
第一章緒論 1
1-1研究動機 1
1-2文獻探討 2
1-3 壓電材料理論 5
1-4論文架構 7
1-5 研究架構 8
1-6本文基本假設 9
第二章 研究方法與內容 10
2-1運動方程式 10
2-1-1研究模型設定 10
2-1-2 位移函數 11
2-1-3 壓電材料之本構方程式 12
壓電材料之力與電之耦合方程式如下： 12
2-1-4 壓電材料應力與應變、應變能、動能 14
2-1-5樑位移、轉角、應力、應變、應變能 17
2-1-6結構運動方程式及邊界條件 18
第三章 整體樑之自由振動分析 22
3-1第一個和第三個跨距的模態法分析 22
3-2第二個跨距的模態法分析 24
3-3求解自然振動頻率 29
3-3-1懸臂樑 29
3-3-2簡支樑 31
第四章 移動負載 32
4-1推導承受移動負載之振動響應方程式 32
4-2 Runge-Kutta法解移動負載方程式 34
第五章 案例探討與數據分析 35
5-1懸臂樑 35
5-1-1 材料設定 35
5-2自然頻率與模態示意圖 36
5-2-1懸臂樑之自然頻率與模態示意圖 36
5-2-2改變壓電材料幾何條件變化影響 37
5-3懸臂樑結構受移動負載速度之動態分析 40
5-3-1改變移動負載速度對自由端位移的變化 41
5-3-2 速度比對結構自由端位移極值之比較 42
5-3-3改變移動負載速度對電荷量收集的變化 43
5-3-4速度比對壓電片收集電荷量極值之比較 44
5-3-5臨界速度下對於結構自由端位移極值之比較 45
5-3-6臨界速度下壓電片收集電荷量極值之比較 48
5-3-7懸臂樑加上電阻改變移動負載速度對自由端位移的變化 51
5-3-8懸臂樑加上電阻改變移動負載速度對電荷量收集的變化 52
5-4動態討論 53
5-4-1改變懸臂樑結構受移動負載速度之動態分析 53
5-5簡支樑 58
5-5-1整體簡支樑之自然頻率與模態示意圖 58
5-5-2改變壓電材料幾何條件變化影響 59
5-6簡支樑結構受移動負載速度之動態分析 62
5-6-1改變移動負載速度對最大位移點位移的變化 63
5-6-2 速度比對結構最大位移點位移極值之比較 64
5-6-3改變移動負載速度對電荷量收集的變化 65
5-6-4速度比對壓電片收集電荷量極值之比較 66
5-6-5臨界速度下對於簡支樑最大位移點位移極值之比較 67
5-6-6臨界速度下對於壓電片收集電荷量極值之比較 70
5-6-7簡支樑加上電阻改變移動負載速度對最大位移點位移的變化 73
5-6-8簡支樑加上電阻改變移動負載速度對電荷量收集的變化 74
5-7動態討論 75
5-7-1改變簡支樑結構受移動負載速度之動態分析 75
第六章 結論與建議 80
6-1 懸臂樑 80
6-1-1自然振動頻率分析 80
6-1-2臨界移動負載速度之動態分析 80
6-1-3動態分析 81
6-2簡支樑 82
6-2-1自然振動頻率分析 82
6-2-2臨界移動負載速度之動態分析 82
6-2-3動態分析 83
6-3建議 84
參考文獻 85
附錄A 87
附錄B 88

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