Binary collision approximation for solitary waves in a Y-shaped granular chain |
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| Authors: | Chen Qiong Yang Xian-Qing Zhao Xin-Yin Wang Zhen-Hui and Zhao Yue-Min |
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| Affiliation: | 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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| Keywords: | Y-shaped granule chain solitary wave binary collision approximation |
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