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

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:
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
Type:
Published Article
Journal Name:
Mathematical Problems in Engineering
Additional Journal Information:
Journal Volume: 2015; Journal Issue: 1; Journal ID: ISSN 1024-123X
Publisher:
Hindawi
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; granular crystals; time-periodic orbits; discrete breathers; Floquet multipliers
OSTI Identifier:
1198644
Alternate Identifier(s):
OSTI ID: 1233184