Timeperiodic solutions of drivendamped trimer granular crystals
Abstract
In this work, we consider timeperiodic 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: SWS. The configuration at the left boundary is driven by a harmonic intime 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 saddlenode 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 fullfield visualizationmore »
 Authors:
 Aristotle Univ. of Thessaloniki, Thessaloniki (Greece); Univ. of Massachusetts, Amherst, MA (United States)
 Univ. of Washington, Seattle, WA (United States)
 Univ. of Massachusetts, Amherst, MA (United States); Swiss Federal Institute of Technology, Zurich (Switzerland)
 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):
 LAUR1428454
Journal ID: ISSN 1024123X; PII: 830978; 830978; TRN: US1600509
 Grant/Contract Number:
 IRSES606096; CMMI1000337; DMS1312856; FA95501210332; CMMI1414748; N000141410388; ESCA 0614; AC5206NA25396
 Resource Type:
 Journal Article: Published Article
 Journal Name:
 Mathematical Problems in Engineering
 Additional Journal Information:
 Journal Volume: 2015; Journal Issue: 1; Journal ID: ISSN 1024123X
 Publisher:
 Hindawi
 Country of Publication:
 United States
 Language:
 English
 Subject:
 36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING; granular crystals; timeperiodic orbits; discrete breathers; Floquet multipliers
Citation Formats
Charalampidis, E. G., Li, F., Chong, C., Yang, J., and Kevrekidis, P. G. Timeperiodic solutions of drivendamped 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. Timeperiodic solutions of drivendamped trimer granular crystals. United States. doi:10.1155/2015/830978.
Charalampidis, E. G., Li, F., Chong, C., Yang, J., and Kevrekidis, P. G. 2015.
"Timeperiodic solutions of drivendamped trimer granular crystals". United States.
doi:10.1155/2015/830978.
@article{osti_1198644,
title = {Timeperiodic solutions of drivendamped 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 timeperiodic 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: SWS. The configuration at the left boundary is driven by a harmonic intime 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 saddlenode 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 fullfield visualization of the timeperiodic structures.},
doi = {10.1155/2015/830978},
journal = {Mathematical Problems in Engineering},
number = 1,
volume = 2015,
place = {United States},
year = 2015,
month = 1
}
Web of Science

In this work, we consider timeperiodic 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: SWS. The configuration at the left boundary is driven by a harmonic intime 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 modesmore »Cited by 3


Spacetime pattern formation and conversion in the dcdriven, damped sineGordon equation
We present results of a numerical and analytical study of the dcdriven, damped sineGordon equation with periodic boundary conditions. We find that this system is characterized by competitions between two classes of multisolitonwavetrain, spacetime structures; phaselocked (cavitymode) states and kinkantikink (fluxonantifluxon) pairs. We also find that a variety of pattern transitions occur between these states. Our results are reported in the language of zerofield steps in annular Josephson junctions and transverse instabilities on propagating interfaces in, e.g., chargedensitywave materials and crystals.