| ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS |
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Binary collision approximation for solitary waves in a Y-shaped granular chain |
| Chen Qiong (陈琼)a, Yang Xian-Qing (杨先清)a, Zhao Xin-Yin (赵新印)a, Wang Zhen-Hui (王振辉)a, Zhao Yue-Min (赵跃民)b |
a College of Science, China University of Mining and Technology, Xuzhou 221116, China;
b School of Chemical Engineering & Technology, China University of Mining and Technology, Xuzhou 221116, China |
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Abstract We implement a binary collision approximation to study solitary wave propagation in a two-dimensional double Y-shaped granular chain. The solitary wave was transmitted and reflected when it met the interface of the bifurcated branches of the Y-shaped granular chains. We obtain analytic results of the ratios of the transmitted and reflected speeds to the incident speed of the solitary wave, the maximum force between two neighbor beads in solitary wave, and the total time took by the pulse to pass through each branch. All of the analytic results are in good agreement with experimental observations by Daraio et al. [Phys. Rev. E 82 036603 (2010)]. Moreover, we also discuss the delay effects on the arrival of split pulses, and predict the recombination of the split waves traveling in branches in the final stem of asymmetric systems. The prediction of pulse recombination is verified by our numerical results.
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Received: 03 June 2012
Revised: 07 July 2012
Accepted manuscript online:
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PACS:
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45.70.-n
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(Granular systems)
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46.40.Cd
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(Mechanical wave propagation (including diffraction, scattering, and dispersion))
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| Fund: Project supported by the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 50921002) and the Fundamental Research Funds for the Central Universities of China (Grant No. 2010LKWL09). |
Corresponding Authors:
Yang Xian-Qing
E-mail: xianqyang@163.com
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Cite this article:
Chen Qiong (陈琼), Yang Xian-Qing (杨先清), Zhao Xin-Yin (赵新印), Wang Zhen-Hui (王振辉), Zhao Yue-Min (赵跃民) Binary collision approximation for solitary waves in a Y-shaped granular chain 2013 Chin. Phys. B 22 014501
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