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Title: Time-Periodic Solutions of Driven-Damped Trimer Granular Crystals

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-periodicmore » structures.« less
Authors:
 [1] ;  [2] ;  [3] ;  [2] ;  [4]
  1. School of Civil Engineering, Faculty of Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece, Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA
  2. Aeronautics & Astronautics, University of Washington, Seattle, WA 98195-2400, USA
  3. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA, Department of Mechanical and Process Engineering (D-MAVT), Swiss Federal Institute of Technology (ETH), 8092 ZΓΌrich, Switzerland
  4. Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515, USA, Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87544, USA
Publication Date:
OSTI Identifier:
1198644
Type:
Published Article
Journal Name:
Mathematical Problems in Engineering
Additional Journal Information:
Journal Volume: 2015; Related Information: CHORUS Timestamp: 2016-08-18 22:22:32; Journal ID: ISSN 1024-123X
Publisher:
Hindawi Publishing Corporation
Sponsoring Org:
USDOE
Country of Publication:
Egypt
Language:
English