非線性二維機構減振研究

On The Vibration Reduction Of a Nonlinear Two-Dimensional Mechanism

張新龍(Hsin-Lung Chang)

指導教授 ： 王怡仁

淡江大學/工學院/航空太空工程學系碩士班/碩士(2008年)

https://doi.org/10.6846/TKU.2008.00951

摘要

本研究考慮二維機翼剖面之振動系統，包含俯仰與上下位移兩自由度，且以一3次方彈簧(cubic spring)為支撐，模擬其非線性的振動現象。並於翼剖面下方懸掛減振裝置，此減振裝置以兩端線性彈簧、阻尼裝設於翼剖面之下，亦包含上下振動及旋轉兩自由度。此外吾人也考慮空氣動力影響，使之形成氣體彈性系統。

為了要驗證本研究結果的正確性，吾人嘗試在頻率域與時間域分析本問題。在時間域方面，吾人使用解析(multiple scales)法，求出此氣體彈性力學系統四自由度解析解。頻率域方面，則直接利用數值解計算出此非線性系統的頻率響應。兩者互相驗證，以確保本模式正確。隨後將調整不同減振器位置以求出最佳位置，而能達到降低系統振幅的最終目的。

關鍵字

非穩態空氣動力學 ； 減振裝置 ； 三次方非線性彈簧

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 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. The analytic model is established by the Newton’s Law. The nonlinear effect is simulated by the cubic spring. The analytic solution is obtained by using the Multiple-Time-Scales method. Some fixed points results (decoupled results) are also studied. The frequency response of this nonlinear system is solved by IMSL© subroutines for comparison. 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 especially for a nonlinear supported mechanism.

並列關鍵字

Unsteady Aerodynamic ； Absorber ； Cubic Spring

參考文獻

[4] 陳柏翰,“二維非線性振動系統減振分析,” 台北縣,淡江

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