非線性阻尼及彈簧振動系統研究與穩定性分析

本研究則是針對剛體的運動，考慮多自由度的耦合現象，以三次方彈簧(cubic spring)及二次方阻尼為支撐，並考慮受到簡單空氣動力影響下，模擬其非線性的振動現象。並於該主體下方懸掛減振裝置為了驗證本研究結果之正確性，吾人以解析及數值兩種方法來分析本研究問題，解析方法方面，吾人以多尺度法(Mutiple Scales法)，求出此氣體彈性系統四自由度之解析解，包含穩態解(steady state solution)及與時間有關的時間態解(time dependend solution)，數值法則為阮奇-庫達(Runge-Kutta)數值積分方法求出頻率振幅分析。並由Floquet法來判斷系統穩定性，提供設計減振機構參考之資訊，隨後調整不同之減振器位置以求出最佳位置，期望能降低系統振幅之最終目的。

關鍵字

非線性阻尼；減振裝置；三次方非線性彈簧；穩定性

並列摘要

A 2-D rigid body nonlinear vibration system is considered in this research. This system includes an attached rigid body absorber. Both main body and the absorber allow plunge and pitch motion. The main body is supported by a cubic spring and a non-linear damper at the body’s elastic axis. Both two ends of the absorber are attached under the main body by linear springs. The unsteady aerodynamic force is also included in this system. This vibration system can be considered a suspension bridge section, an airfoil with pylon, or any other vibration mechanisms with under stores. The main goal of this research is to study the effects of the attached vibration absorber on a vibrating rigid body sustaining aerodynamic force and analysis stability. The analytic model is established by the Newton’s Law. The nonlinear effect is simulated by the cubic spring and nonlinear damper. The analytic solution is obtained by using the Multiple-Time-Scales method. The system stability is obtained by Floquet method. Some fixed points results are also studied. Correlations of both analytic function and numerical results are made and prove the accuracy of our model. The optimal location of this absorber for minimum main body vibration and unsteady motion is concluded in this research. The results of this research provide a better way to reduce system vibration and increasing the stability for system.

並列關鍵字

Nonlinear Damper ； Absorber ； Cubic Spring ； Stability

參考文獻

[7] 張新龍, “非線性二維機構減振研究”, 台北縣,淡江大學航空太空工程系碩士班.

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國際替代計量

非線性阻尼及彈簧振動系統研究與穩定性分析

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