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Published July 19, 2013 | Published
Journal Article Open

Frequency bands of strongly nonlinear homogeneous granular systems


Recent numerical studies on an infinite number of identical spherical beads in Hertzian contact showed the presence of frequency bands [ Jayaprakash, Starosvetsky, Vakakis, Peeters and Kerschen Nonlinear Dyn. 63 359 (2011)]. These bands, denoted here as propagation and attenuation bands (PBs and ABs), are typically present in linear or weakly nonlinear periodic media; however, their counterparts are not intuitive in essentially nonlinear periodic media where there is a complete lack of classical linear acoustics, i.e., in "sonic vacua." Here, we study the effects of PBs and ABs on the forced dynamics of ordered, uncompressed granular systems. Through numerical and experimental techniques, we find that the dynamics of these systems depends critically on the frequency and amplitude of the applied harmonic excitation. For fixed forcing amplitude, at lower frequencies, the oscillations are large in amplitude and governed by strongly nonlinear and nonsmooth dynamics, indicating PB behavior. At higher frequencies the dynamics is weakly nonlinear and smooth, in the form of compressed low-amplitude oscillations, indicating AB behavior. At the boundary between the PB and the AB large-amplitude oscillations due to resonance occur, giving rise to collisions between beads and chaotic dynamics; this renders the forced dynamics sensitive to initial and forcing conditions, and hence unpredictable. Finally, we study asymptotically the near field standing wave dynamics occurring for high frequencies, well inside the AB.

Additional Information

© 2013 American Physical Society. Received 5 October 2012; revised manuscript received 25 March 2013; published 19 July 2013. This work was funded in part by MURI Grant No. US ARO W911NF-09-1-0436 and by the US National Science Foundation, NSF CMMI Grant No. 844540. We acknowledge Dr. Nicholas Boechler for assisting with the initial setup of the experiment.

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Published - PhysRevE.88.012206.pdf


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August 19, 2023
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