Traveling Waves for the Mass in Mass Model of Granular Chains

Academic Article


  • In the present work, we consider the mass in mass (or mass with mass) system of granular chains, namely, a granular chain involving additionally an internal (or, respectively, external) resonator. For these chains, we rigorously establish that under suitable “anti-resonance” conditions connecting the mass of the resonator and the speed of the wave, bell-shaped traveling-wave solutions continue to exist in the system, in a way reminiscent of the results proven for the standard granular chain of elastic Hertzian contacts. We also numerically touch upon settings, where the conditions do not hold, illustrating, in line also with recent experimental work, that non-monotonic waves bearing non-vanishing tails may exist in the latter case.
  • Authors

    Published In

    Digital Object Identifier (doi)

    Author List

  • Kevrekidis PG; Stefanov AG; Xu H
  • Start Page

  • 1067
  • End Page

  • 1088
  • Volume

  • 106
  • Issue

  • 8