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Published February 2013 | Submitted + Published
Journal Article Open

Hysteresis loops and multi-stability: From periodic orbits to chaotic dynamics (and back) in diatomic granular crystals


We consider a statically compressed diatomic granular crystal, consisting of alternating aluminum and steel spheres. The combination of dissipation, driving of the boundary, and intrinsic nonlinearity leads to complex dynamics. Through both numerical simulations and experiments, we find that the interplay of nonlinear surface modes with modes caused by the driver create the possibility, as the driving amplitude is increased, of limit cycle saddle-node bifurcations beyond which the dynamics of the system becomes chaotic. In this chaotic state, part of the applied energy can propagate through the chain. We also find that the chaotic branch depends weakly on the driving frequency, and speculate a connection between the chaotic dynamics with the gap openings between the spheres. Finally, we observe hysteretic dynamics and an interval of multi-stability involving stable periodic solutions and chaotic ones.

Additional Information

© 2013 EPLA. Received 2 November 2012; accepted in final form 20 January 2013; published online 28 February 2013. Support from US-NSF, US-AFOSR and the A.S. Onassis Foundation is appreciated.

Attached Files

Published - 0295-5075_101_4_44003.pdf

Submitted - 1211.1428.pdf


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August 19, 2023
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