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Wave propagation in random granular chains

Mohith Manjunath, Amnaya P. Awasthi, and Philippe H. Geubelle*

  • Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

  • *Present address: 306 Talbot Laboratory, 104 S Wright St, Urbana, Illinois 61801, USA; geubelle@illinois.edu.
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Phys. Rev. E 85, 031308 – Published 29 March, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.031308

Abstract

The influence of randomness on wave propagation in one-dimensional chains of spherical granular media is investigated. The interaction between the elastic spheres is modeled using the classical Hertzian contact law. Randomness is introduced in the discrete model using random distributions of particle mass, Young's modulus, or radius. Of particular interest in this study is the quantification of the attenuation in the amplitude of the impulse associated with various levels of randomness: two distinct regimes of decay are observed, characterized by an exponential or a power law, respectively. The responses are normalized to represent a vast array of material parameters and impact conditions. The virial theorem is applied to investigate the transfer from potential to kinetic energy components in the system for different levels of randomness. The level of attenuation in the two decay regimes is compared for the three different sources of randomness and it is found that randomness in radius leads to the maximum rate of decay in the exponential regime of wave propagation.

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Phys. Rev. E 85, 031308– Published 29 March, 2012
  • Received 18 January 2012

©2012 American Physical Society

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