Open AccessBinary collision approximation for solitary wave in periodic dimer granular chains
Author(s) -
Qiong Chen,
Yang Xian-qing,
Xian-Geng Zhao,
Zhenhui Wang,
Yuemin Zhao
Publication year - 2012
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.61.044501
Subject(s) - radius , chain (unit) , collision , oscillation (cell signaling) , binary number , physics , particle (ecology) , pulse (music) , dimer , computational physics , optics , quantum mechanics , mathematics , nuclear magnetic resonance , chemistry , biochemistry , oceanography , computer security , arithmetic , detector , computer science , geology
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.