研究生: |
彭榮貴 Rong-Gui Peng |
---|---|
論文名稱: |
雙線性分數階微分系統之穩態分析 Steady-State Response of Bilinear Hysteresis System with Fractional Damping |
指導教授: |
黃慶東
Ching-Tung Hung |
口試委員: |
陳瑞華
Rwey-Hua Cherng 鄭蘩 Van Jeng |
學位類別: |
碩士 Master |
系所名稱: |
工程學院 - 營建工程系 Department of Civil and Construction Engineering |
論文出版年: | 2017 |
畢業學年度: | 105 |
語文別: | 中文 |
論文頁數: | 66 |
中文關鍵詞: | 分數階阻尼 、雙線性模型 |
外文關鍵詞: | Fractional Differential, Bilinear hysteresis model |
相關次數: | 點閱:215 下載:0 |
分享至: |
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
本研究探討單自由度雙線性系統加裝分數階阻尼,將分數階微分次數及分數階阻尼係數視為主要變數,其數值介於0至1間,藉由改變主要變數觀察系統穩態(steady-state)反應之變化。本研究利用Newmark法配合電腦運算進行數值分析。結果顯示分數階阻尼具有阻尼及勁度之特質,該特質隨著主要參數的變化而改變。研究過程中發現振幅頻譜圖具有雙峰現象,且穩態反應呈現位移飄移行為,前述現象主要發生在非線性反應下,其中,雙峰現象發生於系統具低頻率比處;位移飄移行為係暫態反應進入非線性所產生之穩態平衡軸偏移,且平衡軸的位置與外力歷時的相位差有關。
This study presents a steady-state response of bilinear fractional damping systems. The order of fractional differential, assumed between 0 and 1, and the fractional damping coefficient are used for parameter studies. The Newmark method is adopted in the numerical analysis. Study results show that the fractional damping possesses the characteristics of damping and stiffness effects that sustantially alter the resulting response. In the nonlinear response, the amplitude spectra show a double-peaked phenomenon where the second peaks occur at low external-to-system frequency ratio. Moreover, the displacement shift in the steady-state response is found due to a non-linear transient response. For those cases, the ultimate steady-state equilibrium position is shifed form the zero position. The equilibrium position is found be to varied as the phase of external force changes.
1. T.K.Caughey, Sinusoidal excitation of a system with bilinear hysteresis, Trans. ASEM, Journal of Applied Mechanics, Series E, 82(1960) 640-643.
2. Miller K.S., Ross B. An introduction to the fractional calculus and fractional differential equations (1993).
3. Gement A. On fractional differences. Phi Mag, 1938, 25 (1):92-96
4. Bagley R L, Torvik P J. Fractional calculus-a different approach to the analysis of viscoelastically damped structures. AIAAJ, 1983, 21(5):741-748.
5. W.D. Iwan, The steady-state response of a two-degree-of-freedom bilinear hysteretic system, Trans. ASME, Journal OF Applied Mechanics, Series E, 87 (1965) 151-156.
6. 楊博翔,“雙線性遲滯系統之雙頻外力反應特性研究”,碩士論文,國立台灣科技大學營建工程系(2009)。
7. 陳鈺承,“分數階微分系統之動力數值分析與探討”,碩士論文,國立台灣科技大學營建工程所 (2013)。
8. 黃心兒,“1/2階微分阻尼系統震動性質之分析”,碩士論文,國立台灣科技大學營建工程所 (2015)。
9. 游俊傑,“分數階微分系統自由震盪反應解析”,碩士論文,國立台灣科技大學營建工程所 (2016)。
10. 王學彬,「求解多項分數皆常微分方程的數值方法」,南屏師專學報,第二十五卷,第四期 (2006)