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

Abstract

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:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE; National Science Foundation (NSF)
OSTI Identifier:
1259964
Report Number(s):
LA-UR-15-21320
Journal ID: ISSN 0377-9017
Grant/Contract Number:  
AC52-06NA25396
Resource 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
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING; Mathematics; Material Science

Citation Formats

Kevrekidis, Panayotis G., Stefanov, Atanas G., and Xu, Haitao. Traveling waves for the mass in mass model of granular chains. United States: N. p., 2016. Web. doi:10.1007/s11005-016-0854-6.
Kevrekidis, Panayotis G., Stefanov, Atanas G., & Xu, Haitao. Traveling waves for the mass in mass model of granular chains. United States. doi:10.1007/s11005-016-0854-6.
Kevrekidis, Panayotis G., Stefanov, Atanas G., and Xu, Haitao. Fri . "Traveling waves for the mass in mass model of granular chains". United States. doi:10.1007/s11005-016-0854-6. https://www.osti.gov/servlets/purl/1259964.
@article{osti_1259964,
title = {Traveling waves for the mass in mass model of granular chains},
author = {Kevrekidis, Panayotis G. and Stefanov, Atanas G. and Xu, Haitao},
abstractNote = {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.},
doi = {10.1007/s11005-016-0854-6},
journal = {Letters in Mathematical Physics},
number = ,
volume = ,
place = {United States},
year = {2016},
month = {6}
}

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    Works referencing / citing this record:

    Waves in strongly nonlinear discrete systems
    journal, July 2018

    • Nesterenko, Vitali F.
    • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 376, Issue 2127
    • DOI: 10.1098/rsta.2017.0130

    Waves in strongly nonlinear discrete systems
    journal, July 2018

    • Nesterenko, Vitali F.
    • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 376, Issue 2127
    • DOI: 10.1098/rsta.2017.0130