硬碟中的軟性印刷電路由如一個彎曲的樑結構，而軟性印刷電路之振動問題亦為影響硬碟運作效率的其中一個重要原因，而先前已有人提出加入阻尼材料做軟性電路減振或以壓電材料控制細長樑結構之振動，無論是阻尼材料的被動減振或是智慧型材料的主動控制減振，均會使軟性電路造成材料不均勻(非均質)之情況，不僅其靜態形狀會改變，其振動行為亦會發生變化，這些議題目前仍沒有學者進行深入探討，而現有之彈性樑模型亦無法預測非均質材料下之靜態形狀。又為了方變對硬碟之軟性電路進行個案之減振設計，使硬碟的製造產線上增加軟性電路之形狀檢測功能，檢測组裝誤差或損壞；以及增加一快速對個案之軟性電路之自然振動模態進行預測之模型。遂本研究以彈簧鋼此線彈性材料，自製五個不同材料比例之非均質試片，以模仿非均質材料下的硬碟軟性電路，且提出一影像擷取系統，以取得非均質試片之靜態形狀；而為了解此非均質試片的振動行為，本研究中依試片之細長特性將其簡化為一維線性樑元素來模擬，建立出一簡化的有限元素分析模型，此模型所預測之非均質試片模態振型和自然共振頻率與實驗量測結果相當接近，並從此模型預測出的自然頻率中發現到，隨著試片材料比例呈現性增加，同一振動模態下之自然頻率似乎呈現非線性的增加；而模型預測出的模態振型之振幅衰減的現象，也發現到可以透過調整試片材料的非均質比例來達到最佳的減振效果。

[1] D. G. Fertis, Nonlinear Structural Engineering: With Unique Theories and Methods to Solve Effectively Complex Nonlinear Problems. New York, NY: Springer Berlin Heidelberg, 2007.
[2] R. Levien, "The elastica: a mathematical history," Technical Report No. UCB/EECS-2008-103, August 23, 2008.
[3] 劉建林, (2013) "細長杆彈性力學模型的發展歷史," 自然雜誌, 卷號 35, pp.372-377, 2013年10月.
[4] A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity, Cambridge, UK: Cambridge University Press, 1928, pp. 242-243.
[5] S. Antman, Nonlinear Problems of Elasticity: New York, NY: Springer Science & Business Media, 2006.
[6] J. Coyne, "Analysis of the formation and elimination of loops in twisted cable," Oceanic Engineering, IEEE Journal of, vol. 15, pp. 72-83, 1990.
[7] Z. Tan, and Witz, J. A., "Loop formation of marine cables and umbilicals during installation," The Biannual Online-Journal of Springsteen Studies, vol. 2., pp. 1270-1285, 1992.
[8] C. Gatti-Bono and N. C. Perkins, "Numerical Simulations of Cable/seabed Interaction," vol. 14, pp. 118-124, 2004.
[9] H. D. Wagner, O. Lourie, and X. F. Zhou, "Macrofragmentation and microfragmentation phenomena in composite materials," Composites Part A: Applied Science and Manufacturing, vol. 30, pp. 59-66, 1999.
[10] S. W. Yoon, N. Yazdi, N. C. Perkins, and K. Najafi, "Micromachined integrated shock protection for MEMS," Sensors and Actuators A: Physical, vol. 130–131, pp. 166-175, 2006.
[11] A. Balaeff, L. Mahadevan, and K. Schulten, "Elastic Rod Model of a DNA Loop in the Lac operon," Physical Review Letters, vol. 83, pp. 4900-4903, 1999.
[12] S. Goyal, T. Lillian, S. Blumberg, J.-C. Meiners, E. Meyhöfer, and N. C. Perkins, "Intrinsic Curvature of DNA Influences LacR-Mediated Looping," Biophysical Journal, vol. 93, pp. 4342-4359, 2007.
[13] S. Goyal and N. C. Perkins, "Looping mechanics of rods and DNA with non-homogeneous and discontinuous stiffness," International Journal of Non-Linear Mechanics, vol. 43, pp. 1121-1129, 2008.
[14] A. M. Bruckstein, R. J. Holt, and A. N. Netravali, "Discrete elastica," Applicable Analysis, vol. 78, pp. 453-485, 2001.
[15] J. Shen, S. Kang, and T. Chan, "Euler's Elastica and Curvature-Based Inpainting," SIAM Journal on Applied Mathematics, vol. 63, pp. 564-592, 2003.
[16] M. R. Brake and J. A. Wickert, "Optimizing Vibration Isolation of Flex Circuits in Hard Disk Drives," Journal of Vibration and Acoustics, vol. 127, pp. 165-172, 2004.
[17] J. A. Wickert, "Vibration of Flex Circuits in Hard Disk Drives," Journal of Vibration and Acoustics, vol. 125, pp. 335-342, 2003.
[18] C-C Chen, and J.-Y. Chang "Profile detection of non-uniform thin flexible interconnect in hard disk drives." Paper presented at ASME/JSME Joint Conference on MIPE, Santa Clara University, CA, USA, 2012.
[19] D. Q. Huynh, "Vibration damped flexible circuit for use in a hard disk drive," The United States Patent 7,414,813, 2008.
[20] J.-Y. Chang, "Hard disk drive seek-arrival vibration reduction with parametric damped flexible printed circuits," Microsystem Technologies, vol. 13, pp. 1103-1106, 2007.
[21] J.-Y. Shen, F-Y Huang, and J. Tian, "Symmetrically tapered constrained layer damper for a flex cable assembly for a hard disk drive," The United States Patent 8,228,639, 2012.
[22] P. Gaudenzi, R. Carbonaro, and E. Benzi, "Control of beam vibrations by means of piezoelectric devices: theory and experiments," Composite Structures, vol. 50, pp. 373-379, 2000.