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:
-
- Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. of Kansas, Lawrence, KS (United States)
- Univ. of Massachusetts, Amherst, MA (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (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. https://doi.org/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. https://doi.org/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 = {Fri Jun 03 00:00:00 EDT 2016},
month = {Fri Jun 03 00:00:00 EDT 2016}
}
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Works referencing / citing this record:
Nonlinear mechanisms of two-dimensional wave-wave transformations in the initially coupled acoustic structure
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