本研究探討圓柱形容器內，在振動下微小顆粒運動之機制，實驗控制參數為振動頻率與振動加速度，研究方向為顆粒的偏析現象、體積濃度和運動機制相圖。實驗首先找出能使大顆粒（鎢顆粒）上升的最小振動加速度，此加速度隨頻率增加而提高，並以此為依據進行顆粒體積濃度的實驗與分析，每個頻率選定數個振動加速度進行實驗，取樣得出鎢顆粒的體積濃度作圖並進行探討，在低頻率時，顆粒床受振動加速度的影響較大，加速度稍微增加，偏析趨勢會有較大的變化，頻率較高則比較緩和。
接著再區分出幾個運動機制，類固體狀態、過渡階段與梯度分佈，當鎢顆粒有如固體般幾乎無運動，稱為鎢顆粒的類固體狀態；若振動強度夠大，鎢顆粒在表層最多，佔有率隨高度降低而遞減，呈現梯度般的排列，為梯度分佈，即本研究所追求的現象；過渡階段則是鎢顆粒上升運動較少，介於類固體狀態與梯度分佈之間的運動現象。

In this study we investigate the size segregation of small particles induced by vertical vibration in a cylinder container. The directions of investigation are segregation phenomena of particles, volume concentration and segregation mechanisms. First, we find the lowest accelerations where tungsten powders can move up. According to the accelerations, the experiments of volume concentration are done. Then we analyze and discuss these results. The influence of acceleration on granular bed is higher at lower frequencies and the one is lower at higher frequencies.
Three mechanisms are defined as solid-like state, transition and gradient distribution. At the solid-like state, tungsten powders in the granular bed behave as a solid. At the gradient distribution regime, the volume concentration of tungsten is decreased with decreasing the height of granular bed and the particle arrangement is in gradient distribution. The transition is the situation between solid-like state and gradient distribution.

[1] Suzuki, K., Hosaka, H., Yamazaki, R., and Jimbo, G., 1980, “Drying Characteristics of Particles in a Constant Drying Rate Period in Vibro-Fluidized Bed,” J. Chem. Engi., Japan, Vol. 13, pp.117-122.
[2] Yu, S. H., Ma, B. J., and Weng, Y. Q., 1992, “Drying Performance and Heat Transfer in a Vibrated Fluidized Beds,” Drying 92, A. S. Mujumdar, ed., Elsevier Science Publishers, Amsterdam, pp. 731-740.
[3] Pakowski, Z., Mujumdar, A. S. and Strumillo, C., 1984, “Theory and Application of Vibrated Beds and Vibrated Fluid Beds for Drying Processes,” Advances in Drying, Vol. 3, A. S. Mujumdar, ed., Hemisphere Publishing, pp. 245-306.
[4] Jaeger, H. M. and Nagel, S. R., 1992, “Physics of the Granular State,” Science, Vol. 255, pp. 1523-1531.
[5] Faraday, M., 1831, “On a Peculiar Class of Acoustical Figures and on Certain Forms Assumed by Groups of Particles upon Vibrating Elastic Surfaces,” Fhil. Trans. R. Soc., London, Vol. 52, pp. 299-340.
[6] Bachmann, D., 1940, Verfahrenstechnik Z.D.I. Beiheft, No. 2, p43 (cited by Thomas et al., 1989)
[7] Knight, J., Jaeger, H. M., and Nagel, S. R., 1993, “Vibration Induced Size Separation in Granular Media: the Convection Connection,” Phys. Rev. Lett., Vol. 70, pp. 3728-3731.
[8] Clement, E., Duran, J., and Rajchenbach, J., 1992, “Experimental Study of Heaping in a Two-Dimensional Sandpile,” Phys. Rev. Lett., Vol. 69, pp.1189-1192.
[9] Savage, S. B. and Lun, C. K., 1988, “Particle Size Segregation in Inclined Chute Flow of Dry Cohesionless Granular Solids,” J. Fluid Mech., Vol. 189, pp. 311-335.
[10] Ehrichs, E., Jaeger, H., Karczmar, G., and Knight, J. B., 1995, “Granular Convection Observed by Magnetic Resonance Imagine,” Science, Vol. 267, pp.1632-1634.
[11] Rosato, A. D. and Lan, Y., 1995, “Macroscopic Behavior of Vibrating Beds of Smooth Inelastic Spheres,” Phys. Fluids., Vol. 7, pp.1818-1831.
[12] Wassgren, C. R., 1997, “Vibration of Granular Materials,” Ph.D. Thesis, California Institute of Technology, California, USA.
[13] Ohtsuki, T., Takemoto, Y., Hata, T., Kawai, S., and Hayash, A., 1993, “Molecular Dynamics Study of Cohesionless Granular Materials: Size Segregation by Shaking,” Int. J. Mod. Phys. B 7, pp.1829-1838.
[14] Thomas, B. and Squires, A. M., 1998, “Confirmation of Faraday´s Explanation of Bunkering in Vibrated Granular Beds,” Powder Technol., Vol. 100, pp. 267-280.
[15] Elperin, T. and Golshtein, E., 1997, “Effects of Convection and Friction on Size Segregation in Vibrated Granular Beds,” Physica A, Vol. 247, pp. 67-78.
[16] Duran, J., Mazozi, T., Clement, E., and Rajchenbach, J., 1994, “Size Segregation in a Two-Dimensional Sandpile: Convecting and Arching Effects,” Phys. Rev. E, Vol. 50, pp. 5138-5141.
[17] Koizumi, M., 1997, “FGM activities in Japan,” Comp. PartB：Engi., Vol. 28, pp. 1-4.
[18] 林遠平，民國88年，“功能梯度材料圓管之熱應力分析”，私立逢甲大學機械工程研究所碩士論文。
[19] Fiscina, J., Ohligschl