Shock Waves in Nonlinear Granular Chain with Viscosity under Hertz Contact

doi:10.7566/JPSJ.88.034002

	Shock Waves in Nonlinear Granular Chain with Viscosity under Hertz Contact
	Zhu, Xiao-Lu 1,2,4; Meng, Zhao-Cang 2; Duan, Wen-Shan 1,4; Yang, Lei2,3 ; Liang, Tao 1,2,4
刊名	JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN
	2019-03-15
卷号	88 期号:3 页码:5
ISSN号	0031-9015
DOI	10.7566/JPSJ.88.034002
通讯作者	Duan, Wen-Shan(duanws@nwnu.edu.cn)
英文摘要	By considering the dependence of the viscosity on the relative velocity between adjacent beads, the shock wave structure in a one-dimensional nonlinear granular system is studied in the present paper. Two different distributions of the shock wave are found. In one distribution, the shock front is a discontinuous surface; in the other, there is an oscillation in the shock front. Furthermore, the wave structure depends on the magnitude of the viscosity and the external impact. There is a critical value of viscosity beta(c). It is found that in the shock front the beads oscillate and the maximum bead velocity is larger than the piston speed if the magnitude of the viscosity is less than beta(c). In contrast, the shock front is a discontinuous surface and the bead velocities are all equal to the piston speed, if the viscosity exceeds beta(c). All numerical results are verified by analytical studies. In the long-wavelength approximation, we obtain a Korteweg-de Vries-Burgers (KdV Burgers) equation that can completely explain the numerical results, and both the numerical and analytical results are in good agreement. This KdV-Burgers equation can be used to study many previous works on both solitary waves and shock waves.
资助项目	Strategic Priority Research Program of the Chinese Academy of Sciences[XDA01020304] ; National Natural Science Foundation of China[11747306] ; National Natural Science Foundation of China[11547304] ; National Natural Science Foundation of China[11647313] ; National Natural Science Foundation of China[11565022]
WOS关键词	SOLITARY WAVES ; PROPAGATION ; LAW
WOS研究方向	Physics
语种	英语
出版者	PHYSICAL SOC JAPAN
WOS记录号	WOS:000460104400007
资助机构	Strategic Priority Research Program of the Chinese Academy of Sciences ; National Natural Science Foundation of China
内容类型	期刊论文
源URL	[http://119.78.100.186/handle/113462/134358]
专题	中国科学院近代物理研究所
通讯作者	Duan, Wen-Shan
作者单位	1.Northwest Normal Univ, Joint Lab Atom & Mol Phys NWNU & IMP CAS, Lanzhou 730070, Gansu, Peoples R China 2.Chinese Acad Sci, Inst Modern Phys, Lanzhou 730000, Gansu, Peoples R China 3.Lanzhou Univ, Dept Phys, Lanzhou 730000, Gansu, Peoples R China 4.Northwest Normal Univ, Coll Phys & Elect Engn, Lanzhou 730070, Gansu, Peoples R China
推荐引用方式 GB/T 7714	Zhu, Xiao-Lu,Meng, Zhao-Cang,Duan, Wen-Shan,et al. Shock Waves in Nonlinear Granular Chain with Viscosity under Hertz Contact[J]. JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN,2019,88(3):5.
APA	Zhu, Xiao-Lu,Meng, Zhao-Cang,Duan, Wen-Shan,Yang, Lei,&Liang, Tao.(2019).Shock Waves in Nonlinear Granular Chain with Viscosity under Hertz Contact.JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN,88(3),5.
MLA	Zhu, Xiao-Lu,et al."Shock Waves in Nonlinear Granular Chain with Viscosity under Hertz Contact".JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN 88.3(2019):5.