本研究使用基礎理論為離散元素法的EDEM離散元素計算軟體，研究二維橢圓長寬比對垂直振動下橢圓顆粒物質之流化現象的影響，使用相同體積但不同長寬比橢圓顆粒，模擬顆粒在垂直振動下的運動行為，從模擬結果得到不同長寬比橢圓顆粒密度對高度關係圖，以及不同橢圓顆粒的流化臨界加速度，排除其他因素的干擾，從中找出橢圓顆粒長寬比與流化現象的關係，結果顯示在振幅0.25 mm、頻率20 Hz、無因次加速度 Γ=4的強烈振動下，流化現象隨橢圓長寬比增加而遞減，而在流化臨界加速度方面，並沒有因為橢圓長寬比的不同而改變，皆大約在無因次加速度 Γ=1.3左右，最後得到流化現象隨橢圓長寬比增加而衰退且在顆粒間交互作用越強情況下越明顯的結論。

In the present study, the EDEM method, based on the discrete element method, is employed to study the effects of the aspect ratio on the surface fluidization in a two-dimensional dry granular matter consisting of elliptic particles in vertical vibration. In the simulations, the aspect ratio of the elliptic is taken as the primary simulation parameter. Results show that the surface fluidization becomes less obvious as the aspect ratio increases. An interesting point is that the critical dimensionless acceleration Γc, which is the minimal acceleration that can trigger the surface fluidization, remains fairly unchanged as the aspect ratio varies.

[1]Reynolds, O. On the Dilatancy of Media Composed of Rigid Particles in Contact. Philos. Mag, 5, 20, 469-481, 1885.
[2]Duran, J. Sands, Powders, and Grains : An Introduction to the Phsics of Granular Materials. Springer, New York, 66-68 (1999).
[3]Chladni, E. F . F. Entdeckungen über die Theorie des Klanges. Leipzig, Germany (1787).
[4]Faraday, M. On a Peculiar Class of Acoustical Figures. Philos. Trans. R. Soc, 52, 299-430, 1831.
[5]Pak ,H. K., Behringer, R.P. Surface Waves in Vertically Vibrated Granular Materials. Phys. Rev. Lett, 71, 1832-1835, 1993.
[6]Dantu, P. Contribution à l'étude mécanique et géométrique des milieux pulvérulents. In Proceedings of the 4th International Conference On Soil Mechanics and Foundation Engineering, 1, 144-148, 1957.
[7]Brown, R. L. The Fundamental Principles of Segregation. J. Inst. Fuel, 13, 15-19, 1939.
[8]Lennard-Jones, J. E. The Determination of Molecular Fields. I. For the Variation of Viscosity of a Gas with Temperature. Proc. Roy. Soc, 106A, 441-462, 1924.
[9]Irving, J. H., Kirkwood, J.G. The Statistical Mechanics of Transport Process. IV. The Equation of Hydrodynamics. J. Chem. Phys, 18, 817-820, 1950.
[10]Alder, B. J., Wainwright, T. E. Phase Transition for a Hard Sphere System. J. Chem. Phys, 27, 1208-1209, 1957.
[11]Stillinger, F. H., Rahman, A. Improved Simulation of liquid Water by Molecular Dynamics. J. Chem. Phys, 60, 1545-1557, 1974.
[12]Pöschel, T., Schwager, T. Computational Granular Dynamics. Springer, Berlin, 13-16 (2005).
[13]Cundall, P. A. A computer model for simulating progressive large scale movements in blocky rock systems. ISRM Symp, 2, 129-136 (1971).
[14]孫其誠、王光謙，顆粒物質力學導論，科學出版社，北京，15-18(2009)。
[15]EDEM 2.0 user guide, DEMSolutions, Edinburgh, 105-106(2008)
[16]Evesque, P., Rajchenbach, J. Instability in a sand heap. Phys. Rev. Lett. 62, 44-46, 1989.
[17]Evesque, P., Szmatula, E., Denis, J.-P. Surface fluidization of a sand pile. Europhys. Lett. 12, 623-627, 1990.
[18]Clément, E., Rajchenbach, J. Fliuidization of a bidimensional powder. Europhys. Lett.16, 133-138, 1991.