本文研究分析軸向運動弦線造成之側向及橫向穩定性的分析及各種參數對於系統振動之影響。本研究主體係以三個自由度的軸向運動橫向振動為主之傳送系統，此系統之運輸帶以一三維之彈性弦線取代並簡化之。而傳輸系統架設在一個不斷有軸向速度的情況下，使此弦線不會因停滯而產生Gyroscope效應的影響。本弦線主體下方以彈簧做為支撐，模擬此弦線置放於elastic foundation 之情況。
吾人使用Lagrange法，分別考量弦線之動能及位能。此外，由於我們考慮的弦線系統假設是一個軸向移動之弦線，其兩端以滾輪固定。在弦線之E.O.M推導出來之後，吾人再以牛頓定理，將弦線之橫向兩個DOF以非線性彈簧支撐之，模擬此弦線埋設於某種彈性介質內。
最後利用四階Runge-Kutta法找出系統之Floquet Transition Matrix，藉由此矩陣便可求得特徵值。吾人代入不同之初始條件，搭配Floquet Multipliers之判定法則，可繪製出系統各運作情況下之Basin of Attraction圖形，藉此觀察系統在不同減振器擺放位置及不同運作情形下之穩定性。

In this paper, we analyze the analysis of lateral and transverse stability caused by axial motion chords and the influence of various parameters on system vibration. In this study, the main system is a three-degree-of-freedom axial motion-based transduction system, which is replaced and simplified by a 3-D elastic string. And the transmission system is erected in a continuous axial velocity, so that the string will not be stagnant and produce Gyroscope effect. The main body of the string below the spring as a support to simulate the string placed in the case of the elastic foundation.
We consider the kinetic energy of the string and bit energy by using Lagrange method. In addition, since the chord system we consider is assumed to be an axially moving string, both ends are fixed with rollers. After deducing the E.O.M of the string, we then use the Newton's theorem to support the two DOF of the string in a non-linear spring to simulate the embedding of the string in a certain elastic medium.
Finally, the fourth-order Runge-Kutta method is used to find the Floquet Transition matrix of the system. The initial condition of the system is different from that of Floquet Multipliers, and the attractive pattern of the system can be drawn. The stability of different shock absorbers and their different operating conditions.

目錄
摘要…………………………………………………………………I
英文摘要……………………………………………………………II
目錄…………………………………………………………………III
圖目錄………………………………………………………………V
第一章	緒論………………………………………………………1
一、1	研究動機…………………………………………………1
一、2   文獻回顧…………………………………………………3
一、3   研究方法…………………………………………………6
第二章	理論模型之建立…………………………………………8
二、1  理論模型之建立……………………………………………8
二、2  非線性運動方程式之推導…………………………………9
二、3  無因次之非線性運動方程式………………………………11
二、4  與相關研究比較本模式之架構……………………………12
第三章	非線性系統之分析……………………………………………14
三、1  多尺度法MOMS求解…………………………………………14
三、2  內共振條件之分析…………………………………………17

三、3  系統之頻率響應……………………………………………21
a、激擾v方向第一模態………………………………………21
b、激擾v方向第四模態………………………………………27
三、4系統之頻率響應分析…………………………………………33
第四章	系統之穩定性分析……………………………………………38
四、1  系統之穩定性………………………………………………38
第五章	結果與討論…………………………………………………41
第六章	結論……………………………………………………………43
參考文獻……..…………………………………………………………44
論文簡要版………………………………………………………………49

圖目錄
圖一 3Dstirng with DVA模擬示意圖………………………………46
圖二 第一模態與第四模態特徵分析圖………………………………20
圖三 簡諧外力激擾v方向第一模態之Fixed Point圖………………47
圖四 簡諧外力激擾v方向第四模態之Fixed Point圖………………47
圖五 系統Basin of Attraction圖…………………………………48

參考文獻
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