非線性支撐雙層基座之減振與內共振特性之研究

本研究提出一種經濟且有效的方法以減少振動基座的振動，並針對該系統之非線性的內共振(Internal Resonance)現象進一步探討之。本振動基座係由上下兩組剛體平板組成，兩平板間的四個角落以非線性彈簧相連接，而下方的平板也在四個角落以非線性彈簧支撐於地面。吾人於各平板下方各掛載兩個單質點減振器，並調整各減振器的位置，以期達到減振的效果。本研究使用Method of Multiple time Scales分析系統的內共振現象，利用特徵值的分析，求取本系統內共振發生的條件。本研究更繪製不同減振器位置所造成的內共振發生機會圖 (Internal Resonance Chart)，並利用數值法繪製其Phase Plot圖形，相互驗證內共振發生條件的正確性。而吾人也藉Phase Plot圖形的收斂振幅大小，以判定各減振器變換位置時，對於本系統各特定自由度振幅的影響，以期歸納出最好的減振器位置，達到減振之效果。本研究發現，本系統中對X軸轉動的自由度與對Y軸轉動的自由度為1:1內共振之情形，在激擾對X軸轉動的自由度時，往往會造成對Y軸轉動自由度的振動頻率變的非常之大，造成系統的不穩定。然而，如果讓減振器的位置儘量的達到對稱分佈的話，將可減少1:1內共振之發生。吾人也發現，減振器如果都置於靠近原點處，其發生內共振的機會較置於靠近端點處為高。此外，吾人將兩顆單質點減振器置於上平板，沿2-4象限方向對稱擺置，以及另兩顆單質點減振器置於下平板原點，對於X、Y軸轉動自由度的振動皆有良好抑制效果。而若將減振器置於原點時，對於上下振動之自由度有較佳之減振效果。由於本文考慮其磁頭置於上方之外力(對X、Y軸旋轉)，以及風扇造成的外力(下方上下振動)，因此對於此情形而言，是將上方減振器置於2-4象限方向之端點(對X、Y軸旋轉最佳)，下方減振器至於原點(對上下振動最佳)，有最佳之減振效果。

關鍵字

非線性；減振器；內共振；相位圖

並列摘要

Without changing the main configuration of the double-decker vibration system, this research presents an economic and efficient way to reduce the vibration of this double-decker system, via change the position of the under attached absorbers. The internal resonance phenomenon in the system is also studied. In this double-decker system, the upper and lower deck is connected with nonlinear spring at each end points of the plate. The lower deck and the ground is supported by the nonlinear spring at each end points of the plate. We add two single point-mass absorbers under each upper and lower deck. By changing the positions of absorbers, we can find out the best locations of the absorbers to reduce the rigid plate vibration. In this research, we use Method of Multiple time Scales to analyze this nonlinear system. We also plot the Internal Resonance chart with different positions of absorbers. The Internal Resonance chart gives information for the locations of absorbers to cause internal resonance. This result can be correlated by the phase plot. From phase plot, we confirm the predictions of the Internal Resonance chart. The eigen-value analysis conducts that this system has an 1:1 internal resonance. However, from the Internal Resonance chart and phase plot analysis, we found that without changing the main configuration of this double-decker system, the best location of the dual-absorber is attached under the plate’s end points of diagonals.

並列關鍵字

Nonlinear ； Absorber ； Internal Resonance ； Phase Plot

參考文獻

[15] 王怡仁，林漢翔， “二維端點支撐之非線性振動系統研究，” 2010中華民國航空太空學術研討會，桃園開南大學，中華民國九十九年十二月四日。

[1] Zuo, L. and Nayfeh, S. A., ’’Minimax Optimization of Multi-Degree-of-Freedom Tuned-Mass Dampers, ” Journal of Sound and Vibration 272, 2004, pp. 893–908.

[2] Heo, Jin Wook and Chung, Jintai, ” Vibration and Noise Reduction of an Optical Disk Drive by Using a Vibration Absorber,” IEEE Transactions on Consumer Electronics, Vol. 48, No. 4, 2002, pp.874-878.

[3] Chung, Jintai,”Vibration Absorber for Reduction of the In-plane Vibration in an Optical Disk Drive” IEEE Transactions on Consumer Electronics, Vol. 50, No. 2, 2004, pp.552-557.

[4] Nayfeh, A.H., ”Introduction to Perturbation Techniques”, Wiley-Interscience, New York, 1981, pp.107-131

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非線性支撐雙層基座之減振與內共振特性之研究

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