TY - JOUR
T1 - Breather arrest, localization, and acoustic non-reciprocity in dissipative nonlinear lattices
AU - Mojahed, Alireza
AU - Gendelman, Oleg V.
AU - Vakakis, Alexander F.
N1 - Funding Information:
This work was supported in part by National Science Foundation Grant No. CMMI-17-1727761. Any opinion, findings, and conclusions or recommendations expressed in this work are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Publisher Copyright:
© 2019 Acoustical Society of America.
PY - 2019/7/1
Y1 - 2019/7/1
N2 - The effect of on-site damping on breather arrest, localization, and non-reciprocity in strongly nonlinear lattices is analytically and numerically studied. Breathers are localized oscillatory wavepackets formed by nonlinearity and dispersion. Breather arrest refers to breather disintegration over a finite "penetration depth" in a dissipative lattice. First, a simplified system of two nonlinearly coupled oscillators under impulsive excitation is considered. The exact relation between the number of beats (energy exchanges between oscillators), the excitation magnitude, and the on-site damping is derived. Then, these analytical results are correlated to those of the semi-infinite extension of the simplified system, where breather penetration depth is governed by a similar law to that of the finite beats in the simplified system. Finally, motivated by the experimental results of Bunyan, Moore, Mojahed, Fronk, Leamy, Tawfick, and Vakakis [Phys. Rev. E 97, 052211 (2018)], breather arrest, localization, and acoustic non-reciprocity in a non-symmetric, dissipative, strongly nonlinear lattice are studied. The lattice consists of repetitive cells of linearly grounded large-scale particles nonlinearly coupled to small-scale ones, and linear intra-cell coupling. Non-reciprocity in this lattice yields either energy localization or breather arrest depending on the position of excitation. The nonlinear acoustics governing non-reciprocity, and the surprising effects of existence of linear components in the coupling nonlinear stiffnesses, in the acoustics, are investigated.
AB - The effect of on-site damping on breather arrest, localization, and non-reciprocity in strongly nonlinear lattices is analytically and numerically studied. Breathers are localized oscillatory wavepackets formed by nonlinearity and dispersion. Breather arrest refers to breather disintegration over a finite "penetration depth" in a dissipative lattice. First, a simplified system of two nonlinearly coupled oscillators under impulsive excitation is considered. The exact relation between the number of beats (energy exchanges between oscillators), the excitation magnitude, and the on-site damping is derived. Then, these analytical results are correlated to those of the semi-infinite extension of the simplified system, where breather penetration depth is governed by a similar law to that of the finite beats in the simplified system. Finally, motivated by the experimental results of Bunyan, Moore, Mojahed, Fronk, Leamy, Tawfick, and Vakakis [Phys. Rev. E 97, 052211 (2018)], breather arrest, localization, and acoustic non-reciprocity in a non-symmetric, dissipative, strongly nonlinear lattice are studied. The lattice consists of repetitive cells of linearly grounded large-scale particles nonlinearly coupled to small-scale ones, and linear intra-cell coupling. Non-reciprocity in this lattice yields either energy localization or breather arrest depending on the position of excitation. The nonlinear acoustics governing non-reciprocity, and the surprising effects of existence of linear components in the coupling nonlinear stiffnesses, in the acoustics, are investigated.
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U2 - 10.1121/1.5114915
DO - 10.1121/1.5114915
M3 - Article
C2 - 31370643
AN - SCOPUS:85070057893
SN - 0001-4966
VL - 146
SP - 826
EP - 842
JO - Journal of the Acoustical Society of America
JF - Journal of the Acoustical Society of America
IS - 1
ER -