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Title: Time-periodic solutions of driven-damped trimer granular crystals

Abstract

In this work, we consider time-periodic structures of granular crystals consisting of alternate chrome steel (S) and tungsten carbide (W) spherical particles where each unit cell follows the pattern of a 2:1 trimer: S-W-S. The configuration at the left boundary is driven by a harmonic in-time actuation with given amplitude and frequency while the right one is a fixed wall. Similar to the case of a dimer chain, the combination of dissipation, driving of the boundary, and intrinsic nonlinearity leads to complex dynamics. For fixed driving frequencies in each of the spectral gaps, we find that the nonlinear surface modes and the states dictated by the linear drive collide in a saddle-node bifurcation as the driving amplitude is increased, beyond which the dynamics of the system becomes chaotic. While the bifurcation structure is similar for solutions within the first and second gap, those in the first gap appear to be less robust. We also conduct a continuation in driving frequency, where it is apparent that the nonlinearity of the system results in a complex bifurcation diagram, involving an intricate set of loops of branches, especially within the spectral gap. The theoretical findings are qualitatively corroborated by the experimental full-field visualizationmore » of the time-periodic structures.« less

Authors:
 [1];  [2];  [3];  [2];  [4]
  1. Aristotle Univ. of Thessaloniki, Thessaloniki (Greece); Univ. of Massachusetts, Amherst, MA (United States)
  2. Univ. of Washington, Seattle, WA (United States)
  3. Univ. of Massachusetts, Amherst, MA (United States); Swiss Federal Institute of Technology, Zurich (Switzerland)
  4. Univ. of Massachusetts, Amherst, MA (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1198644
Alternate Identifier(s):
OSTI ID: 1233184
Report Number(s):
LA-UR-14-28454
Journal ID: ISSN 1024-123X; PII: 830978; 830978; TRN: US1600509
Grant/Contract Number:  
IRSES-606096; CMMI1000337; DMS1312856; FA9550-12-1-0332; CMMI1414748; N000141410388; ESC-A 06-14; AC52-06NA25396
Resource Type:
Journal Article: Published Article
Journal Name:
Mathematical Problems in Engineering
Additional Journal Information:
Journal Volume: 2015; Journal Issue: 1; Journal ID: ISSN 1024-123X
Publisher:
Hindawi
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING; granular crystals; time-periodic orbits; discrete breathers; Floquet multipliers

Citation Formats

Charalampidis, E. G., Li, F., Chong, C., Yang, J., and Kevrekidis, P. G. Time-periodic solutions of driven-damped trimer granular crystals. United States: N. p., 2015. Web. doi:10.1155/2015/830978.
Charalampidis, E. G., Li, F., Chong, C., Yang, J., & Kevrekidis, P. G. Time-periodic solutions of driven-damped trimer granular crystals. United States. doi:10.1155/2015/830978.
Charalampidis, E. G., Li, F., Chong, C., Yang, J., and Kevrekidis, P. G. Thu . "Time-periodic solutions of driven-damped trimer granular crystals". United States. doi:10.1155/2015/830978.
@article{osti_1198644,
title = {Time-periodic solutions of driven-damped trimer granular crystals},
author = {Charalampidis, E. G. and Li, F. and Chong, C. and Yang, J. and Kevrekidis, P. G.},
abstractNote = {In this work, we consider time-periodic structures of granular crystals consisting of alternate chrome steel (S) and tungsten carbide (W) spherical particles where each unit cell follows the pattern of a 2:1 trimer: S-W-S. The configuration at the left boundary is driven by a harmonic in-time actuation with given amplitude and frequency while the right one is a fixed wall. Similar to the case of a dimer chain, the combination of dissipation, driving of the boundary, and intrinsic nonlinearity leads to complex dynamics. For fixed driving frequencies in each of the spectral gaps, we find that the nonlinear surface modes and the states dictated by the linear drive collide in a saddle-node bifurcation as the driving amplitude is increased, beyond which the dynamics of the system becomes chaotic. While the bifurcation structure is similar for solutions within the first and second gap, those in the first gap appear to be less robust. We also conduct a continuation in driving frequency, where it is apparent that the nonlinearity of the system results in a complex bifurcation diagram, involving an intricate set of loops of branches, especially within the spectral gap. The theoretical findings are qualitatively corroborated by the experimental full-field visualization of the time-periodic structures.},
doi = {10.1155/2015/830978},
journal = {Mathematical Problems in Engineering},
number = 1,
volume = 2015,
place = {United States},
year = {Thu Jan 01 00:00:00 EST 2015},
month = {Thu Jan 01 00:00:00 EST 2015}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1155/2015/830978

Citation Metrics:
Cited by: 3 works
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