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標題: | 應用系統識別技術估算強非線性系統自由振盪頻率 On the estimation of the frequency of free vibration of strong nonlinear system using system identification technique |
作者: | Sheng-Hsiang Lin 林聖翔 |
指導教授: | 柯文俊 |
關鍵字: | 系統識別,達芬方程,數值次空間運算法,非線性振動, system identification,Duffing equation,N4SID,nonlinear vibration, |
出版年 : | 2007 |
學位: | 碩士 |
摘要: | 嚴格說起來,自然界的振動現象皆為非線性振動。因為一切的力學系統都含有非線性因子,其中的差別在於非線性程度的多寡。由於非線性微分方程還沒有一套普遍有效的定量求解方法。早期研究非線性振動的理論分析方法多侷限於弱非線性振動系統,碰到強非線性振動系統就顯的無能為力。因此近二十年來研究非線性振動領域的各派學者致力於提出各種新理論分析方法,使其能適用於分析強弱非線性振動系統。
而本文拜現代電腦運算速度之賜,提出利用數值計算方法求解出非線性振動系統之輸出響應。並對此輸出響應以系統識別技術中的數值次空間運算法(N4SID),來做強弱非線性振動系統之定量分析研究。分析過程中並以時間歷時圖、功率頻譜密度圖、時譜圖及模態穩定圖來輔助觀察分析。最後由分析結果顯示,本文所提出的應用系統識別技術來分析強弱非線性系統係一可行之方法。 Strictly speaking, the vibration phenomenon of the nature is all nonlinear vibration. Because all mechanics systems contain the nonlinear factor, the difference between them is how much nonlinearity the system has. Nowadays there has no good way to quantitatively determine nonlinear equation. There are various techniques for constructing analytical approximations to the nonlinear differential equation. But many of them apply to weakly nonlinear cases only. To overcome the limitations, many novel techniques have been proposed to solve strong nonlinear case in recent 20 years. With the rapid development of the modern computer, this paper proposed using numerical analysis to obtain the reopens of nonlinear system. Then identify the nonlinear system by using N4SID method. Besides, the analysis of the process also utilizes time history diagram, power spectrum density diagram and modal stabilization diagram to assist the research. The results obtained from the proposing method reveal the technique of system identification is a new way to analyzing strong or weak nonlinear system. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/27477 |
全文授權: | 有償授權 |
顯示於系所單位: | 工程科學及海洋工程學系 |
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