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Effect of wall friction on subharmonic bifurcations of impact in vertically vibrated granular beds

Han Hong Jiang Ze-Hui Li Xiao-Ran Lü Jing  Zhang Rui Ren Jie-Ji

Effect of wall friction on subharmonic bifurcations of impact in vertically vibrated granular beds

Han Hong, Jiang Ze-Hui, Li Xiao-Ran, Lü Jing,  Zhang Rui, Ren Jie-Ji
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  • 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.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10974038).
    [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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 56 3727]

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  • Received Date:  06 December 2012
  • Accepted Date:  15 February 2013
  • Published Online:  05 June 2013

Effect of wall friction on subharmonic bifurcations of impact in vertically vibrated granular beds

  • 1. Department of Physics, Harbin Institute of Technology, Harbin 150001, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 10974038).

Abstract: 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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