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Binary collision approximation for solitary wave in periodic dimer granular chains

Chen Qiong Yang Xian-Qing Zhao Xin-Yin Wang Zhen-Hui Zhao Yue-Min

Binary collision approximation for solitary wave in periodic dimer granular chains

Chen Qiong, Yang Xian-Qing, Zhao Xin-Yin, Wang Zhen-Hui, Zhao Yue-Min
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  • Received Date:  27 May 2011
  • Accepted Date:  01 September 2011
  • Published Online:  05 February 2012

Binary collision approximation for solitary wave in periodic dimer granular chains

  • 1. College of Science, China University of Mining and Technology, Xuzhou 221116, China;
  • 2. School of Chemical Engineering & Technology, China University of Mining and Technology, Xuzhou 221116, China
Fund Project:  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 (Grant No. 2010LKWL09).

Abstract: We study solitary wave propagation in periodic dimer granular chains of beads with the same material but different sizes by binary collision approximation. This kind of chain which is called N:1 dimer consists of pairs of N big beads and one small bead. First we present a method to map the actual chain into an effective chain, then use the binary collision approximation to obtain the transmitted solitary wave speed, the total time taken by the pulse to pass through the chain, and the frequency of oscillation of the small particle. Frequency of oscillation, which increases with the decrease of the radius of the small particle, is analytically obtained. And the results are in excellent agreement with numerical results. For the total time of the pulse passing through the chain, the results of theoretical analysis is in good agreement with numerical results when N 2. The relative error seems no change with the chain length but becomes larger with the increase of the value of N.

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