Eur. Phys. J. E (2019) 42: 140
https://doi.org/10.1140/epje/i2019-11904-x

Regular Article

Scattering of shock wave by impurities in a viscoelastic granular chain

College of Physics and Electronic Engineering and Joint Laboratory of Atomic and Molecular Physics of NWNU & IMP CAS, Northwest Normal University, 730070, Lanzhou, China

^* e-mail: liangtao0623@126.com
^** e-mail: duanws@nwnu.edu.cn

Received: 18 December 2018
Accepted: 14 October 2019
Published online: 8 November 2019

Abstract

The transmission and the reflection of a shock wave by one or several impurities in viscoelastic bead chains is studied in the present paper. There is only one reflected wave for a single impurity. The amplitude of the beads oscillation increases as the initial velocity of the boundaries beads increases, while it decreases as the viscosity coefficient increases. Two reflected waves will be produced if the impurity number is larger than a critical value. This critical value depends on both the initial velocity and the viscosity coefficient. In addition, the maximum amplitude of reflected wave is a constant, when the viscosity coefficient is large enough.