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颗粒物质由离散的固体颗粒组成, 受到周期性振动时可以表现出复杂的动力学行为. 这些行为往往受众多因素的影响, 如空气阻力和器壁摩擦力等. 针对受振颗粒体系中冲击力的倍周期分岔现象, 通过抽真空或将容器底镂空消除空气阻力, 单独研究器壁滑动摩擦力的影响. 结果表明在仅有器壁摩擦力作用的情况下, 倍周期分岔过程仅受约化振动加速度的控制, 与颗粒的尺寸、颗粒层数及振动频率无关. 将器壁摩擦力处理成一个大小恒定、方向与颗粒和器壁相对速度反向的阻力, 并包含到完全非弹性蹦球模型中, 能够对所观察到的现象给出很好的解释. 通过对倍周期分岔点测量平均值的拟合, 得到器壁滑动摩擦力的大小约为颗粒总重量的10%.Granular materials consist of a large number of discrete solid particles. When subjected to external vibrations, they exhibit various intricate dynamical behaviors, Which usually depend in a complicated way on many physical factors, such as air dragging, friction from the container wall and so forth. In this work, vertical vibrations are applied to a bed of stainless-steel spheres contained in a glass tube, and the subharmonic bifurcations of impact of particles on the container bottom are investigated. To eliminate the effects of air dragging, we evacuate the container or perforate the container bottom to make it quite permeable to the air. Experiments performed in such containers reveal that the impact bifurcations are controlled solely by the normalized vibration acceleration, but independent of the particle size, the filling height of particles, and the frequency of forced vibration. The sliding friction from the container wall is treated as a constant one with the direction opposite to the velocity relative to the container wall. By involving this damping term into the completely inelastic bouncing ball model, an explanation for the experimental results is made. Simulations on the averaged experimental bifurcation points indicate that the magnitude of wall friction is about 10% of the total weight of the particles.
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Keywords:
- granular materials /
- wall friction /
- subharmonic bifurcations /
- impact
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[12] Pastor J M, Maza D, Zuriguel I, Garcimartin A, Boudet J F, 2007 Physica D 232 128
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[22] Horváth V K, Jánosi I M, Vella P J 1996 Phys. Rev. E 54 2005
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[24] Peng Z, Wang L Z, Jiang Y M 2011 J. Shandong Univ. Nat. Sci. 46 42 [彭政, 王璐珠, 蒋亦民 2011 山东大学学报 (理学版) 46 42]
[25] Géminard J C, Losert W, Gollub J P 1999 Phys. Rev. E 59 5881
[26] Divoux T, Geminard J C 2007 Phys. Rev. Lett. 99 258301
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[29] Jiang Z H, Jing Y F, Zhao H F, Zheng R H 2009 Acta Phys. Sin. 58 5923 (in Chinese) [姜泽辉, 荆亚芳, 赵海发, 郑瑞华 2009 58 5923]
[30] Jiang Z H, Zhang F, Guo B, Zhao H F, Zheng R H 2010 Acta Phys. Sin. 59 5581 (in Chinese) [姜泽辉, 张锋, 郭波, 赵海发, 郑瑞华 2010 59 5581]
[31] Cheng Y F, Guo S J, Lai H Y 2000 Powder. Technol. 107 123
[32] Rhodes M, Takeuchi S, Liffman K, Muniandy K 2003 Granul. Matter. 5 107
[33] Luck J M, Metha A 1993 Phys. Rev. E 48 3988
[34] Gilet T, Vandewalle N, Dorbolo S 2009 Phys. Rev. E 79 055201
[35] Jiang Z H, Zheng R H, Zhao H F, Wu J 2007 Acta Phys. Sin. 56 3727 (in Chinese) [姜泽辉, 郑瑞华, 赵海发, 吴晶 2007 56 3727]
-
[1] Duran J 2000 Sands powders and grains: An introduction to the physics of granular materials (New York: Springer-Verlag)
[2] de Gennes P G 1999 Rev. Mod. Phys. 71 374
[3] Sperl M 2006 Granul. Matter. 8 59
[4] Peng Z, Li X Q, Jiang L, Fu L P, Jiang Y M 2009 Acta Phys. Sin. 58 2090 (in Chinese) [彭政, 李湘群, 蒋礼, 符力平, 蒋亦民 2009 58 2090]
[5] Radjai F, Jean M, Moreau J J, Roux S 1996 Phys. Rev. Lett. 77 274
[6] Knight J B, Jaeger H M, Nagel S R 1993 Phys. Rev. Lett. 70 3728
[7] Knight J B, Ehrichs E E, Kuperman V Y, Flint J K, Jaeger H M, Nagel S R1996 Phys. Rev. E 54 5726
[8] Melo F, Umbanhowar P B, Swinney H L 1995 Phys. Rev. Lett. 75 3838
[9] Bizon C, Shattuck M D, Swift J B, McCormick W D, Swinney H L 1998 Phys. Rev. Lett. 80 57
[10] Douady S, Fauve S, Laroche C 1989 Europhys. Lett. 8 621
[11] Jiang Z H, Liu X Y, Peng Y J, Li J W 2005 Acta Phys. Sin. 54 5692 (in Chinese) [姜泽辉, 刘新影, 彭雅晶, 李建伟 2005 54 5692]
[12] Pastor J M, Maza D, Zuriguel I, Garcimartin A, Boudet J F, 2007 Physica D 232 128
[13] Jiang Z H, Wang Y Y, Wu J 2006 Europhys. Lett. 74 417
[14] Jiang Z H, Wang Y Y, Wu J 2006 Acta Phys. Sin. 55 4748 (in Chinese) [姜泽辉, 王运鹰, 吴晶 2006 55 4748]
[15] Pak H K, Van Doorn E, Behringer R P 1995 Phys. Rev. Lett. 74 4643
[16] Liu C, Wang L, Wu P, Jia M 2010 Phys. Rev. Lett. 104 188001
[17] Aoki K M, Akiyama T, Yamamoto K, Yoshikawa T 1997 Europhys. Lett. 40 159
[18] Elperin T, Golshtein E 1997 Physica A 247 67
[19] Gallas J A C, Herrmann H J, Sokolowski S 1992 Phys. Rev. Lett. 69 1371
[20] Akiyama T, Kimura N, Iguchi T 1996 Powder. Technol. 89 133
[21] Jiang Z H, Guo B, Zhang F, Wang F L 2010 Acta Phys. Sin. 59 8444 (in Chinese) [姜泽辉, 郭波, 张峰, 王福力 2010 59 8444]
[22] Horváth V K, Jánosi I M, Vella P J 1996 Phys. Rev. E 54 2005
[23] Hu L, Yang P, Xu T, Jiang Y, Xu H L, Long W, Yang C S, Zhang S, Lu K Q 2003 Acta Phys. Sin. 52 879 (in Chinese) [胡林, 杨平, 徐亭, 江阳, 须海江, 龙为, 杨昌顺, 张弢, 陆坤权 2003 52 879]
[24] Peng Z, Wang L Z, Jiang Y M 2011 J. Shandong Univ. Nat. Sci. 46 42 [彭政, 王璐珠, 蒋亦民 2011 山东大学学报 (理学版) 46 42]
[25] Géminard J C, Losert W, Gollub J P 1999 Phys. Rev. E 59 5881
[26] Divoux T, Geminard J C 2007 Phys. Rev. Lett. 99 258301
[27] Wassgren C R, Brennen C E, Hunt M L 1996 J. Appl. Mech. 63 712
[28] Hsiau S S, Pan S J 1998 Powder. Technol. 96 219
[29] Jiang Z H, Jing Y F, Zhao H F, Zheng R H 2009 Acta Phys. Sin. 58 5923 (in Chinese) [姜泽辉, 荆亚芳, 赵海发, 郑瑞华 2009 58 5923]
[30] Jiang Z H, Zhang F, Guo B, Zhao H F, Zheng R H 2010 Acta Phys. Sin. 59 5581 (in Chinese) [姜泽辉, 张锋, 郭波, 赵海发, 郑瑞华 2010 59 5581]
[31] Cheng Y F, Guo S J, Lai H Y 2000 Powder. Technol. 107 123
[32] Rhodes M, Takeuchi S, Liffman K, Muniandy K 2003 Granul. Matter. 5 107
[33] Luck J M, Metha A 1993 Phys. Rev. E 48 3988
[34] Gilet T, Vandewalle N, Dorbolo S 2009 Phys. Rev. E 79 055201
[35] Jiang Z H, Zheng R H, Zhao H F, Wu J 2007 Acta Phys. Sin. 56 3727 (in Chinese) [姜泽辉, 郑瑞华, 赵海发, 吴晶 2007 56 3727]
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