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    Please use this identifier to cite or link to this item: https://ir.lib.ksu.edu.tw/handle/987654321/6856

    Title: 微分轉換於非線動力問題及其混沌現象之研究
    A study on nonlinearly dynamic problems and their chaotic phenomena using differential transform
    Authors: 何星輝
    Keywords: 非線性動力問題
    Nonlinear dynamic problems
    Limit cycle
    Phase plane
    Differential transform
    Inverse differential transform
    T spectrum
    Chaotic motion
    Poincare' map
    Lyapunov exponent
    Power spectrum analysis
    Date: 2001-07-31
    Issue Date: 2009-12-31 15:43:02 (UTC+8)
    Abstract: 本計劃旨在提出一個新方法--微分轉換法,來進行非線性動力問題及其混沌現象之基礎性研究。非線性動力問題普遍存在於工程實務問題上,以往之研究大多以數值方法,例如Newmark method 、Runge-Kutta method ; 近似方法, 例如Perturbation method、KBM method 求解。使用數值方法須經大量的疊代運算及計算機時間,而使用近似方法則須經歷煩瑣的推衍,方可求得近似解。使用本計劃所提之微分轉換法配合T 譜貯存法,可使求解過程大為簡化,不須經大量的疊代運算及計算機時間即可求得多項式型式之解答。混沌現象是非線性動力問題的自然延伸,有關混沌運動的研究大多以Poincare映射、功率譜分析、 Lyapunov 指數、奇異吸子維數等方法為之;在本計劃中擬以相平面及T 譜進行混沌分析。使用微分轉換法求解非線性動力問題及其混沌現象,必須將函數之定義域加以分割,是而步長與項數會影響計算結果準確性與收斂性;如何決定最佳之步長與項數亦是研究目標之一。
    In this project, we propose a new method --differential transform-- to engage in the basic study on nonlinear dynamic problems and their chaotic phenomena. There are many nonlinear dynamic problems in engineering fields. These problems can be solved by a few numerical methods such as Newmark method, Runge-Kutta method etc., or by approximate mehods such as perterbation method, KMB method etc.. The solutions obtained by the numerical methods usually undergo a lot of iterations and require a lot of CPU time. The solutions obtained by the approximate methods usually undergo complicated derivations. Using differential transform and T spectrum storage method, we simplify the solving processes and obtain the polynomial form solutions with no iterations and less CPU time. Chaotic phenomena are the extension of nonlinear dynamic behaviors. There are many previous works using Poincare map, power spectrum, Lyapunov exponent, the dimension of strange attractor, etc. to study chaos. Using phase plane and T spectrum obtained from differential transform, we try to engage in the basic study on chaos. Using differential transform to study nonlinear dynamic problems and their chaotic phenomena, we should split the function domain to speed up the convergent rate and accuracy of calculation. How to decide the optimum step length and terms number is also an object of the project.
    Appears in Collections:[機械工程系所] 研究計畫

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