摩擦力对非弹性蹦球倍周期运动的影响

姜泽辉; 郭波; 张峰; 王福力

doi:10.7498/aps.59.8444

摘要

分析了摩擦力对竖直振动台面上完全非弹性蹦球动力学行为的影响.当控制参数Γ由1逐渐增大时,作用在蹦球上的恒定摩擦力不会改变倍周期分岔的序列,但会使倍周期分岔点的数值变大.与无摩擦力时的情况相比,在飞行时间的分岔图中也存在倍周期分岔密集区,只是被横向拉伸纵向压缩,且具有不同的分形特性.与受振颗粒体系中的倍周期分岔过程做了比较,发现当摩擦力取值为颗粒总重量的20%—30%时两者符合很好.

关键词:

蹦球 /
颗粒物质 /
倍周期分岔 /
分形

The behavior of a completely inelastic ball bouncing on a vertically vibrating table in the presence of frictional force is investigated. The frictional force is assumed to be constant. It is found that the sequence of bifurcation, controlled solely by the normalized vibration acceleration Γ, is the same as that in the absence of frictional force, but the value of each bifurcation point becomes larger. In the bifurcation diagram of ball flight time, the structure consisting of an infinity of bifurcation cascades in a narrow range of Γ is observed. Compared with that of no frictional force, it is longitudinally compressed and transversely stretched, and has a different fractal property. A comparison with the bifurcations observed in vertically vibrated granular beds is also made. When the fractional force is set to be 20%—30% of the whole weight of the particles, the results from the bouncing ball model are in good agreement with experimental observations.

Keywords:

作者及机构信息

1.
哈尔滨工业大学物理系,哈尔滨 150001

基金项目: 国家自然科学基金(批准号:10974038,10674035)资助的课题.

Authors and contacts

1.
Department of Physics, Harbin Institute of Technology, Harbin 150001, China

参考文献

[1]	Tufillaro N B, Abbott T, Reilly J 1992 An Experimental Approach to Nonlinear Dynamics and Chaos (New York: Addison-Wesley Publishing Company)
[2]	Pierański P 1988 Phys. Rev. A 37 1782
[3]	Holmes P J 1982 J. Sound Vib. 84 173
[4]	Mehta A, Luck J M 1990 Phys. Rev. Lett. 65 393
[5]	Luck J M, Mehta A 1993 Phys. Rev. E 48 3988
[6]	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]
[7]	Jiang Z H, Zhao H F, Zheng R H 2009 Acta Phys. Sin. 58 7579 (in Chinese)[姜泽辉、赵海发、郑瑞华 2009 58 7579]
[8]	Gilet T, Vandewalle N, Dorbolo S 2009 Phys. Rev. E 79 055201
[9]	Melo F, Umbanhowar P B, Swinney H L 1995 Phys. Rev. Lett. 75 3838
[10]	Moon S J, Shattuck M D, Bizon C, Goldman D I, Swift J B, Swinney H L 2001 Phys. Rev. E 65 11301
[11]	Luding S, Clément E, Blumen A, Rajchenbach J, Duran J 1994 Phys. Rev. E 49 1634
[12]	Douady S, Fauve S, Laroche C 1989 Europhys. Lett. 8 621
[13]	Wassgren C R, Brennen C E, Hunt M L 1996 J. Appl. Mech. 63 712
[14]	Aoki K M, Akiyama T, Yamamoto K, Yoshikawa T 1997 Europhys. Lett. 40 159
[15]	Jiang Z H, Wang Y Y, Wu J 2006 Europhys. Lett. 74 417
[16]	Jiang Z H, Li B, Zhao H F, Wang Y Y, Dai Z B 2005 Acta Phys. Sin. 54 1273 (in Chinese)[姜泽辉、李斌、赵海发、王运鹰、戴智斌 2005 54 1273] 〖17] 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]
[17]	Pastor J M, Maza D, Zuriguel I, Garcimartín A, Boudet J F 2007 Physica D 232 128
[18]	Ho C K, Webb S W 2006 Gas Transport in Porous Media (Dordrecht: Springer) pp5—26
[19]	Nield D A, Bejan A 2006 Convection in Porous Media (3rd ed) (New York: Springer) Chap 1
[20]	Pak H K, Doorn E V, Behringer R P 1995 Phys. Rev. Lett. 74 4643
[21]	Yan X, Shi Q, Hou M, Lu K, Chan C K 2003 Phys. Rev. Lett. 91 14302
[22]	Mbius M E, Cheng X, Eshuis P, Karczmar G S, Nagel S R, Jaeger H M 2005 Phys. Rev.E 72 011304
[23]	Akiyama T, Kimura N, Iguchi T 1996 Powder Technol. 89 133
[24]	Akiyama T, Yoshikawa T 1999 Powder Technol. 103 139
[25]	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]
[26]	Evasque P, Szmatula E, Denis J P 1990 Europhys. Lett. 12 623
[27]	Knight J B, Jaeger H M, Nagel S R 1993 Phys. Rev. Lett. 70 3728
[28]	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]
[29]	Zeilstra C, Collignon J G, van der Hoef M A, Deen N G, Kuipers J A M 2008 Powder Technol. 184 166

施引文献

[1]	Tufillaro N B, Abbott T, Reilly J 1992 An Experimental Approach to Nonlinear Dynamics and Chaos (New York: Addison-Wesley Publishing Company)
[2]	Pierański P 1988 Phys. Rev. A 37 1782
[3]	Holmes P J 1982 J. Sound Vib. 84 173
[4]	Mehta A, Luck J M 1990 Phys. Rev. Lett. 65 393
[5]	Luck J M, Mehta A 1993 Phys. Rev. E 48 3988
[6]	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]
[7]	Jiang Z H, Zhao H F, Zheng R H 2009 Acta Phys. Sin. 58 7579 (in Chinese)[姜泽辉、赵海发、郑瑞华 2009 58 7579]
[8]	Gilet T, Vandewalle N, Dorbolo S 2009 Phys. Rev. E 79 055201
[9]	Melo F, Umbanhowar P B, Swinney H L 1995 Phys. Rev. Lett. 75 3838
[10]	Moon S J, Shattuck M D, Bizon C, Goldman D I, Swift J B, Swinney H L 2001 Phys. Rev. E 65 11301
[11]	Luding S, Clément E, Blumen A, Rajchenbach J, Duran J 1994 Phys. Rev. E 49 1634
[12]	Douady S, Fauve S, Laroche C 1989 Europhys. Lett. 8 621
[13]	Wassgren C R, Brennen C E, Hunt M L 1996 J. Appl. Mech. 63 712
[14]	Aoki K M, Akiyama T, Yamamoto K, Yoshikawa T 1997 Europhys. Lett. 40 159
[15]	Jiang Z H, Wang Y Y, Wu J 2006 Europhys. Lett. 74 417
[16]	Jiang Z H, Li B, Zhao H F, Wang Y Y, Dai Z B 2005 Acta Phys. Sin. 54 1273 (in Chinese)[姜泽辉、李斌、赵海发、王运鹰、戴智斌 2005 54 1273] 〖17] 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]
[17]	Pastor J M, Maza D, Zuriguel I, Garcimartín A, Boudet J F 2007 Physica D 232 128
[18]	Ho C K, Webb S W 2006 Gas Transport in Porous Media (Dordrecht: Springer) pp5—26
[19]	Nield D A, Bejan A 2006 Convection in Porous Media (3rd ed) (New York: Springer) Chap 1
[20]	Pak H K, Doorn E V, Behringer R P 1995 Phys. Rev. Lett. 74 4643
[21]	Yan X, Shi Q, Hou M, Lu K, Chan C K 2003 Phys. Rev. Lett. 91 14302
[22]	Mbius M E, Cheng X, Eshuis P, Karczmar G S, Nagel S R, Jaeger H M 2005 Phys. Rev.E 72 011304
[23]	Akiyama T, Kimura N, Iguchi T 1996 Powder Technol. 89 133
[24]	Akiyama T, Yoshikawa T 1999 Powder Technol. 103 139
[25]	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]
[26]	Evasque P, Szmatula E, Denis J P 1990 Europhys. Lett. 12 623
[27]	Knight J B, Jaeger H M, Nagel S R 1993 Phys. Rev. Lett. 70 3728
[28]	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]
[29]	Zeilstra C, Collignon J G, van der Hoef M A, Deen N G, Kuipers J A M 2008 Powder Technol. 184 166

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