多減振器排列位置於振動平板減振之研究

Vibration Reduction of the Formation of Multiple-TMDs on a Vibration Rigid Plate

陳政憶(Cheng-Yi Chen)

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(2013年)

https://doi.org/10.6846/TKU.2013.01228

摘要

本研究考慮一個三維剛體平板，假設其四端以三次方非線性彈簧及線性阻尼支撐，並於上方附加一扭矩彈簧來模擬主體之共面旋轉 ，以建構一非線性振動體，而主體下方則懸掛多個二自由度 (2 Degrees of Freedom) 線性彈簧的調質式減振器 (Tuned Mass Damper) ，並且使用減振器不同位置的排列方式，來尋找抑制主體振幅之最有效的組合。基於本研究為非線性系統，因此吾人利用時間多尺度法 (Method of Multiple Scales (MOMS) ) ， 將非線性運動方程式分成兩個不同的尺度，由於分解後的尺度仍具有時間項的係數，於是吾人再針對方程式做一次 MOMS法，接著找出系統各自由度之振動頻率。最後藉由各排列組合之各自由度的頻率響應圖，找出最佳的排列幾何圖形，以能大幅減少主體振幅來擁有最佳的減振效果。

關鍵字

非線性振動 ； 多尺度法 ； 調質式減振器

並列摘要

This study proposed an economical and effective method of reducing vibration in a rigid-plate mechanism. The prime vibrating mechanism comprised a rigid body plate joined by a cubic nonlinear spring at each of the four corners to simulate a transversal and out-of-plane vibration of the plate. A torsional spring was also attached to simulate the in-plane torsional vibration. Four combinations of multiple TMDs (plate edge lined, plate cross, plate edged box, and plate diagonal lined locations) were attached under the plate. Lagrange’s equation was used to derive the motion of the rigid plates. Vibration reduction effect was studied analytically and numerically following attachment of the TMD at different fixed positions in the system. We employed the method of multiple scales (MOMS) to find the fixed points solutions and the associated frequency responses. The numerical simulation was carried on by the RK-4 method. Both numerical and analytical solutions agreed with each other. The results show that the box or cross combinations of multiple TMDs locations reveal the most effective in reducing the amplitude of vibrations of the plates, when the force was applied on the 1st quadrant or the plate origin

並列關鍵字

Nonlinear vibration ； Method of multiple scales ； Tuned mass damper

參考文獻

[21] 王怡仁、羅仲延,“混合式動態平衡減振器之設計及研究”,淡江大學航空太空工程學系碩士班碩士論文,中華民國一百零二年一月.

[3] Den Hartog, J. P., Mechanical Vibration , 1947, McGraw–Hill.

[5] Joshi, A. S. and Jangid, R. S., “Optimum parameters of multiple tuned mass dampers for base - excited damped systems,” Journal of Sound and Vibration, Vol. 202, 1997, pp.657–667.

[6] Zuo, L. and Nayfeh, S. A., “Minimax optimization of multi-degree- of-freedom tuned-mass dampers,” Journal of Sound and Vibration, Vol. 272, 2004, pp.893–908.

[7] Li, Hong-Nan and Ni, Xiang-Lei, “Optimization of non-uniformly distributed multiple tuned mass damper,” Journal of Sound and Vibration, Vol. 308, 2007, pp.80–97.