Traveling waves and their tails in locally resonant granular systems
In the present study, we revisit the theme of wave propagation in locally resonant granular crystal systems, also referred to as massinmass 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 nonvanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of antiresonance conditions is identified for which solutions with genuinely rapidly decaying tails arise.
 Authors:

^{[1]};
^{[2]};
^{[3]}
 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:
 Report Number(s):
 LAUR1429563
Journal ID: ISSN 17518113; TRN: US1600510
 Grant/Contract Number:
 1313107; DMS1312856; 2010239; 605096; FA95501210332; AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Physics A: Mathematical and Theoretical
 Additional Journal Information:
 Journal Volume: 48; Journal Issue: 19; Journal ID: ISSN 17518113
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING
 OSTI Identifier:
 1233282
 Alternate Identifier(s):
 OSTI ID: 1239032
Xu, H., Kevrekidis, P. G., and Stefanov, A.. Traveling waves and their tails in locally resonant granular systems. United States: N. p.,
Web. doi:10.1088/17518113/48/19/195204.
Xu, H., Kevrekidis, P. G., & Stefanov, A.. Traveling waves and their tails in locally resonant granular systems. United States. doi:10.1088/17518113/48/19/195204.
Xu, H., Kevrekidis, P. G., and Stefanov, A.. 2015.
"Traveling waves and their tails in locally resonant granular systems". United States.
doi:10.1088/17518113/48/19/195204. 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 massinmass 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 nonvanishing tails at both ends of the computational domain. Importantly, however, a countably infinite set of antiresonance conditions is identified for which solutions with genuinely rapidly decaying tails arise.},
doi = {10.1088/17518113/48/19/195204},
journal = {Journal of Physics A: Mathematical and Theoretical},
number = 19,
volume = 48,
place = {United States},
year = {2015},
month = {4}
}