臺灣博碩士論文加值系統

本文探討一桿件承受等速移動質量塊之振動模擬與穩定性分析，進而探討此類系統之動態吸振器(DVA)設計。文中首先建立系統模型，模型中將系統分解成二個次系統，一為水平桿件承受一移動力，另一為等速移動質塊承受一橫向移動力。利用漢米爾頓定理(Hamilton’s principle)推導出運動方程式，再運用模態展開法(modes expansion method)將方程式離散化，此為週期時變運動方程式。
在數值分析中，動態分析應用朗格庫塔數值法(Runge-Kutta Mathod)獲得系統之響應，續將求出的響應值利用FFT分析系統的響應頻率變化。吾人發現系統有一主要響應頻率，系統主要響應頻率在低速時會與當質塊固定在桿件中間時系統自然頻率接近，隨著質量塊越重而響應頻率分布範圍越大，隨著速度增加系統主要響應頻率也會改變。本文利用佛洛昆特理論(Floquet theory)觀察系統的不穩定範圍，其不穩定區隨質塊質量越重範圍越廣。文末在系統上加入一質量彈簧動態吸振器，透過吸振指標找出DVA最好的設定頻率，並探討參數對DVA設定頻率之影響，且整理得到參數對DVA設定頻率之函數。

This thesis deals with the vibration and the stability of a simply supported uniform beam subject to a moving mass at a constant velocity. The governing equations eventually become a periodic time-varying system. Furthermore, the design of dynamic vibration absorber on such a system is explored. In this study, Hamilton’s principle is first used to derive the equations of motion, then, the modes expansion method yields the discrete equation of motions.
In the numerical analysis, Runge-Kutta Method is used to find the dynamic responses and Fast Fourier Transform is used to find the response frequencies. The results show that there is a main response frequency. At low moving speeds, the main response frequency is close to the one as the moving mass fixed at the middle of the beam. As speed increases, the response frequency deviates from it. In the stability analysis, Floquet theory is used to observe the unstable area. The results show that increasing of moving mass also increases the unstable area.
In the end of the research, the problems of a dynamic vibration absorber tacked on-to the system are discussed. A power absorber index is defined to find the best setting frequency of the DVA. A dimensionless best setting frequency for DVA is then developed.

摘要 I
ABSTRACT II
誌謝 III
目錄 IV
圖表索引 VI
第一章 緒論 1
1.1文獻回顧 1
1.2 研究動機與目的 4
1.3 本文架構 5
第二章 系統運動方程式 9
2.1 建立系統模型 9
2.2 系統運動方程式推導 10
2.3系統運動方程式之離散化 13
2.4具DVA系統之運動方程式推導 15
第三章 振動分析 20
3.1系統響應－朗格庫塔數值方法 20
3.2 穩定性分析－佛洛昆特理論 23
3.3 簡例示範 28
第四章 具DVA系統之振動分析 41
4.1 吸振指標 41
4.2簡例示範及參數探討 42
第五章 結論與未來研究方向 60
5.1 結論 60
5.2 未來研究方向與建議 63
參考文獻 65
作者簡介 68

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