Traveling waves and their tails in locally resonant granular systems
Abstract
In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as mass-in-mass systems. We use three distinct approaches to identify relevant traveling waves. In addition, the first consists of a direct solution of the traveling wave problem. The second one consists of the solution of the Fourier tranformed variant of the problem, or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) in real space. Finally, our third approach will restrict considerations to a finite domain, utilizing the notion of Fourier series for important technical reasons, namely the avoidance of resonances, which will be discussed in detail. All three approaches can be utilized in either the displacement or the strain formulation. Typical resulting computations in finite domains result in the solitary waves bearing symmetric non-vanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of anti-resonance conditions is identified for which solutions with genuinely rapidly decaying tails arise.
- Authors:
-
- Univ. of Massachusetts, Amherst, MA (United States)
- Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Univ. of Kansas, Lawrence, KS (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1233282
- Alternate Identifier(s):
- OSTI ID: 1239032
- Report Number(s):
- LA-UR-14-29563
Journal ID: ISSN 1751-8113; TRN: US1600510
- Grant/Contract Number:
- 1313107; DMS1312856; 2010239; 605096; FA9550-12-10332; AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Physics. A, Mathematical and Theoretical
- Additional Journal Information:
- Journal Volume: 48; Journal Issue: 19; Journal ID: ISSN 1751-8113
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING
Citation Formats
Xu, H., Kevrekidis, P. G., and Stefanov, A. Traveling waves and their tails in locally resonant granular systems. United States: N. p., 2015.
Web. doi:10.1088/1751-8113/48/19/195204.
Xu, H., Kevrekidis, P. G., & Stefanov, A. Traveling waves and their tails in locally resonant granular systems. United States. https://doi.org/10.1088/1751-8113/48/19/195204
Xu, H., Kevrekidis, P. G., and Stefanov, A. Wed .
"Traveling waves and their tails in locally resonant granular systems". United States. https://doi.org/10.1088/1751-8113/48/19/195204. https://www.osti.gov/servlets/purl/1233282.
@article{osti_1233282,
title = {Traveling waves and their tails in locally resonant granular systems},
author = {Xu, H. and Kevrekidis, P. G. and Stefanov, A.},
abstractNote = {In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as mass-in-mass systems. We use three distinct approaches to identify relevant traveling waves. In addition, the first consists of a direct solution of the traveling wave problem. The second one consists of the solution of the Fourier tranformed variant of the problem, or, more precisely, of its convolution reformulation (upon an inverse Fourier transform) in real space. Finally, our third approach will restrict considerations to a finite domain, utilizing the notion of Fourier series for important technical reasons, namely the avoidance of resonances, which will be discussed in detail. All three approaches can be utilized in either the displacement or the strain formulation. Typical resulting computations in finite domains result in the solitary waves bearing symmetric non-vanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of anti-resonance conditions is identified for which solutions with genuinely rapidly decaying tails arise.},
doi = {10.1088/1751-8113/48/19/195204},
journal = {Journal of Physics. A, Mathematical and Theoretical},
number = 19,
volume = 48,
place = {United States},
year = {Wed Apr 22 00:00:00 EDT 2015},
month = {Wed Apr 22 00:00:00 EDT 2015}
}
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Works referencing / citing this record:
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