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題名 | 兩個勢井的Duffing系統受雙外力激振之週期運動與混沌響應=Periodic and Chaotic Responses in a Twin-Well Duffing System Subjected to Two External Excitations |
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作者 | 簡守謙; Jen, Shoou-chian; |
期刊 | 應用聲學與振動學刊 |
出版日期 | 20101000 |
卷期 | 2:2 2010.10[民99.10] |
頁次 | 頁113-119 |
分類號 | 446.8 |
語文 | chi |
關鍵詞 | Mellnikov方法; 分歧圖; 雙頻率激振; 混沌; Melnikov's method; Bifurcation; Two external excitations; Chaos; |
中文摘要 | 本論文分析兩個勢井的Duffing系統受雙外力頻率激振之週期運動與混沌響應。首先以Melnikov解析方法,求取Duffing系統受雙頻率激振時,週期運動與混沌響應的臨界參數值。其次以數值模擬分析,在吸子盆地(Basins of attraction),穩態解的起始值是以基本週期交替出現之特性。取多個初始條件之分歧圖,有出現週期三(period-3)響應,並呈現週期倍增至混沌;配合以相圖、頻譜圖、Poincarè切面圖、響應時序圖和Lyapunov指數,證明分歧圖在參數變化之穩態響應之型態。 |
英文摘要 | Periodic and chaotic responses in the twin-welll Duffing system subjected to two external excitations are investigated. First, the boundary of periodic and chaotic motion under the periodic perturbation is determined by using Melnikov's method. Second, using numerical integration, based on 4th order Runge-Kutta method is used to simulate Duffing system for various initial conditions and parameters. As bifurcation diagrams are plotted, frequency-locked oscillations with period-3 motion and cascades of period-doubling to chaos are found. Numerical simulations including homoclinic bifurcation surfaces, bifurcation diagrams, Poincaré maps, phase portraits, frequency spectra and maximum Lyapunov exponents are given to illustrate the theoretical analysis. |
本系統之摘要資訊系依該期刊論文摘要之資訊為主。