非線性支撐基座之減振與穩定性研究

過往減振設計，以改變減振器之質量或直接在基座支撐點使用減振材料使其具有減振效果。但如此之設計，因應不同的系統需要不同的減振器，這樣將大大增加成本。故在本研究中，我們將使用一種更符合經濟成本，且在不改變減振器材料及更動光碟機之大部分架構的方式之下，僅以改變減振器位置的方法來達到減振與穩定的效果。此外，本研究將基座四個角落的彈性係數與阻尼係數作非線性化假設，並加入二個獨立之點質量減振器，運用Lagrangian Method導出其運動方程，再以複合時間比例法(Multiple Scales)求其穩態固定點(Fixed Points)的頻率愈響應和解析解，再運用Floquet Method找出其線性化系統特徵值，利用特徵值特性判斷系統之穩定性，並以耦合模式之相位圖數值解與解析解加以對照佐證此模式及結果的正確性。本研究除了使用雙質點減振系統之外，對於許多非線性的現象也有分析，其結果將是線性假設所無法發現的；對於雙質點減振器擺放位置之於系統減振效果與穩定性，也詳加研究，相信可有效降低振動幅度與找出穩定範圍，期望成果能對相關產業作為測試、設計之參考。

關鍵字

光碟機；振動；減振器；非線性；穩定性

並列摘要

In this research, an optimized position of a set of 2 mass-spring-damper vibration absorbers is proposed for a vibration mechanism device (such as optical disk drive or other mechanical vibration deck system). This vibration system is simulated by a rigid body deck with 4 corners supported by cubic springs and square dampers. Only out-of-plane motions are considered in this research. 2 point-mass absorbers are attached under this deck. A nonlinear 3-D theoretical model for this system is established by Lagrange’s equation. The analytical solution is obtained by the multiple time scale method. The IMSL © subroutine is employed for solving nonlinear system frequency response. The fixed points semi-analytic results in frequency domain are also acquired. The Floquet-method can apply a simply stability analysis. It is found that the existing vibration deck amplitude can be reduced by simply adding the absorbers at the end corner of the deck, without changing the main configurations.It is also found that the stability can be transformed by changing different position of the absorbers. This will not only save costs but also increase testing efficiency, achieving the most cost-effective vibration reduction result. This research provides a theoretical background for the preliminary vibration reduction design for industries.

並列關鍵字

CD-ROM, Vibration ； Absorber ； Nonlinear ； Stability

參考文獻

[17]張銘祥, “非線性支撐基座之減振研究,” 淡江大學航空太空工程學所碩士論文(2008).

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

[2] Alexander, N.A. and Schilder, F., “Exploring the performance of a nonlinear tuned mass damper,” Journal of Sound and Vibration 319, 2009, 445–462.

[3] Winterflood, J., Barber, T. and Blair, D.G., “Using Euler buckling springs for vibration isolation,” Classical and Quantum Gravity 19, 2002, 1639-1645.

[4] Heo, J.W. and Chung, J., “Vibration and Noise Reduction of an Optical Disk Drive by Using a Vibration Absorber,” IEEE Transactions on Consumer Electronics 48(4), 2002, 874-878.

國際替代計量

非線性支撐基座之減振與穩定性研究

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