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Title: Nonlinear resonances and antiresonances of a forced sonic vacuum

Abstract

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.

Authors:
 [1];  [2];  [1];  [2];  [3];  [2];  [1]
+ Show Author Affiliations
  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)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1246363
Alternate Identifier(s):
OSTI ID: 1233896
Report Number(s):
LA-UR-15-24544
Journal ID: ISSN 1539-3755; PLEEE8
Grant/Contract Number:  
US ARO W911NF-09-1-0436; FA9550-12-1-0332; AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Additional Journal Information:
Journal Volume: 92; Journal Issue: 6; Journal ID: ISSN 1539-3755
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING

Citation Formats

Pozharskiy, D., Zhang, Y., Williams, M. O., McFarland, D. M., Kevrekidis, P. G., Vakakis, A. F., and Kevrekidis, I. G. Nonlinear resonances and antiresonances of a forced sonic vacuum. United States: N. p., 2015. Web. doi:10.1103/PhysRevE.92.063203.
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Pozharskiy, D., Zhang, Y., Williams, M. O., McFarland, D. M., Kevrekidis, P. G., Vakakis, A. F., & Kevrekidis, I. G. Nonlinear resonances and antiresonances of a forced sonic vacuum. United States. https://doi.org/10.1103/PhysRevE.92.063203
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Pozharskiy, D., Zhang, Y., Williams, M. O., McFarland, D. M., Kevrekidis, P. G., Vakakis, A. F., and Kevrekidis, I. G. Wed . "Nonlinear resonances and antiresonances of a forced sonic vacuum". United States. https://doi.org/10.1103/PhysRevE.92.063203. https://www.osti.gov/servlets/purl/1246363.
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@article{osti_1246363,
title = {Nonlinear resonances and antiresonances of a forced sonic vacuum},
author = {Pozharskiy, D. and Zhang, Y. and Williams, M. O. and McFarland, D. M. and Kevrekidis, P. G. and Vakakis, A. F. and Kevrekidis, I. G.},
abstractNote = {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.},
doi = {10.1103/PhysRevE.92.063203},
url = {https://www.osti.gov/biblio/1246363}, journal = {Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics},
issn = {1539-3755},
number = 6,
volume = 92,
place = {United States},
year = {2015},
month = {12}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1103/PhysRevE.92.063203
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