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This content will become publicly available on August 1, 2017

Title: Traveling waves for the mass in mass model of granular chains

In this 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. Finally, 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:
 [1] ;  [2] ;  [3]
  1. Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Univ. of Kansas, Lawrence, KS (United States)
  3. Univ. of Massachusetts, Amherst, MA (United States)
Publication Date:
OSTI Identifier:
1259964
Report Number(s):
LA-UR-15-21320
Journal ID: ISSN 0377-9017
Grant/Contract Number:
AC52-06NA25396
Type:
Accepted Manuscript
Journal Name:
Letters in Mathematical Physics
Additional Journal Information:
Journal Name: Letters in Mathematical Physics; Journal ID: ISSN 0377-9017
Publisher:
Springer
Research Org:
Los Alamos National Laboratory (LANL)
Sponsoring Org:
USDOE; National Science Foundation (NSF)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING Mathematics; Material Science