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Time-Periodic Solutions of Driven-Damped Trimer Granular Crystals
Joint Authors
Charalampidis, E. G.
Li, F.
Chong, C.
Yang, J.
Kevrekidis, P. G.
Source
Mathematical Problems in Engineering
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-07-09
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Charalampidis, E. G.& Li, F.& Chong, C.& Yang, J.& Kevrekidis, P. G.. 2015. Time-Periodic Solutions of Driven-Damped Trimer Granular Crystals. Mathematical Problems in Engineering،Vol. 2015, no. 2015, pp.1-15.
https://search.emarefa.net/detail/BIM-1074841
Modern Language Association (MLA)
Charalampidis, E. G.…[et al.]. Time-Periodic Solutions of Driven-Damped Trimer Granular Crystals. Mathematical Problems in Engineering No. 2015 (2015), pp.1-15.
https://search.emarefa.net/detail/BIM-1074841
American Medical Association (AMA)
Charalampidis, E. G.& Li, F.& Chong, C.& Yang, J.& Kevrekidis, P. G.. Time-Periodic Solutions of Driven-Damped Trimer Granular Crystals. Mathematical Problems in Engineering. 2015. Vol. 2015, no. 2015, pp.1-15.
https://search.emarefa.net/detail/BIM-1074841
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1074841