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題名 | 線性與非線性正規模態之比較與應用=Comparisons and Applications of Linear and Nonlinear Normal Modes |
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作者 | 李新欉; Lee, Hsin-tsrong; |
期刊 | 新新科技年刊 |
出版日期 | 20070100 |
卷期 | 3 2007.01[民96.01] |
頁次 | 頁134-144 |
分類號 | 440.15 |
語文 | chi |
關鍵詞 | 線性正規模態; 非線性正規模態; 非線性振動; Linear normal modes; Nonlinear normal modes; Nonlinear vibration; |
中文摘要 | 結構系統振動的正規模態分析一直都是模態分析、模態測試及模態控制及模態識別所研究的重點之一。線性結構系統正規模態分析的傳統作法,是經由特徵方程式求解來加以獲得,這對於離散系統相當有用,但對於線性連續系統的偏微分方程式或者非線性系統則無法運用。本文參考前人對不變流形(invariant manifold)的研究,將其理論與作法運用於線性離散及連續系統的正規模態求解問題上,同時亦將其推廣至非線性離散及連續系統,探討在平衡點附近運動的非線性正規模態。從線性與非線性離散及連續系統正規模態的比較中得知,線性正規模態的位移比值為常數,而非線性正規模態的位移比值與位移振幅有關,另非線性正規模態的振頻也與位移振幅有關。 |
英文摘要 | Normal modes analysis of the vibratory system is one of the important research areas among model analysis, model testing, modal control and modal identification. The traditional method for obtaining the normal modes of the vibratory system is solved by characteristic equations. The method is useful only for linear discrete systems and it fails in applications for linear continuous systems and nonlinear discrete and continuous systems. This article presents a new method for obtaining normal modes based on invariant manifold and has been proving successfully for examples of linear and nonlinear discrete and continuous systems. From comparisons of linear and nonlinear normal modes, it concludes that the displacement ratio of two distinct linear normal modes is a constant and the displacement ratio and oscillating frequencies of two nonlinear normal modes are dependent upon the amplitude of displacement. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。