本文討論非線性振動系統之吸振器動態及轉動系統模化，對於吸振器之討論，以不對稱非線性振動系統為數學模型。整體架構大略為以下步驟： 首先推導其振動模式，包含主振系統及吸振器部分之非線性振動方程式。然後分析此二系統之動態特性，使用分析工具為 Harmonic Balance， Floquet Theory。六組不同系統參數造成各種不同之動態行為，結果在較高頻區域有二或三區塊顯示分歧現象(Bifurcation Phenomena)，並在共存區之鞍點-節點分歧現象裏，主要共振區右側峰值為存在於吸振器之操作頻帶，其分析結果說明新的共存現象發生於很強的非線性系統。之後處理穩定性的問題，更深入探討系統之變化，隨參數之改變，完整描述系統動態結構的轉變。最後為模化的探討，本文的方法為使用不平衡引發之旋轉力，計算其輸入作用力及輸出振幅間相角關係，以完成其參數判別。利用根軌跡及Floquet-Liapunov 理論，驗證其穩定性分析結果，再從電腦模擬結果與實驗比較，證明此種方法之可行性。

ABSTRACT
In this study, we concern with the dynamics behavior of nonlinear vibration system that contain absorber and modeling of a rotating system. For the absorber system, a mathematical model of an asymmetrically nonlinearity is proposed. The analytical work on this nonlinear vibration absorber was performed by the harmonic balance method using Floquet theory. We analyze six cases of dynamic phenomena with various system parameters. Two or three unstable regions show bifurcation phenomena at a high vibration frequency. The right peak of the primary resonance of the saddle-node bifurcation in the region of coexistence is close to the bandwidth of the absorber. The results demonstrate that new phenomena will occur in a strongly nonlinear system. For the system modeling, the centrifugal force induced by an unbalanced mass is used as the input signal, and the phase between the input signal and the measured output vibration amplitude is calculated to perform the identification. Stability analysis and system performance are evaluated by using the root locus and the Floquet-Liapunov theorem. A comparison between the simulation results and some experimented data shows the feasibility of the proposed approach.

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