Nonlinear resonances and antiresonances of a forced sonic vacuum

Journal Article · Wed Dec 23 00:00:00 EST 2015 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

DOI:https://doi.org/10.1103/PhysRevE.92.063203· OSTI ID:1246363

Pozharskiy, D. ^[1]; Zhang, Y. ^[2]; Williams, M. O. ^[1]; McFarland, D. M. ^[2]; Kevrekidis, P. G. ^[3]; Vakakis, A. F. ^[2]; Kevrekidis, I. G. ^[1]

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1. Princeton Univ., Princeton, NJ (United States)
2. Univ. of Illinois at Urbana-Champaign, Urbana, IL (United States)
3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Massachusetts, Amherst, MA (United States)

We consider a harmonically driven acoustic medium in the form of a (finite length) highly nonlinear granular crystal with an amplitude- and frequency-dependent boundary drive. Despite the absence of a linear spectrum in the system, we identify resonant periodic propagation whereby the crystal responds at integer multiples of the drive period and observe that this can lead to local maxima of transmitted force at its fixed boundary. In addition, we identify and discuss minima of the transmitted force (“antiresonances”) between these resonances. Representative one-parameter complex bifurcation diagrams involve period doublings and Neimark-Sacker bifurcations as well as multiple isolas (e.g., of period-3, -4, or -5 solutions entrained by the forcing). We combine them in a more detailed, two-parameter bifurcation diagram describing the stability of such responses to both frequency and amplitude variations of the drive. This picture supports a notion of a (purely) “nonlinear spectrum” in a system which allows no sound wave propagation (due to zero sound speed: the so-called sonic vacuum). As a result, we rationalize this behavior in terms of purely nonlinear building blocks: apparent traveling and standing nonlinear waves.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: US ARO W911NF-09-1-0436; FA9550-12-1-0332; AC52-06NA25396
• OSTI ID: 1246363
• Alternate ID(s): OSTI ID: 1233896
• Report Number(s): LA-UR-15-24544; PLEEE8
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Vol. 92, Issue 6; ISSN 1539-3755
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
97 MATHEMATICS AND COMPUTING