Abstract
We study a class of strongly nonlinear traveling waves and localized modes in one-dimensional homogeneous granular chains with no precompression. Until now the only traveling-wave solutions known for this class of systems were the single-hump solitary waves studied by Nesterenko in the continuum approximation limit. Instead, we directly study the discrete strongly nonlinear governing equations of motion of these media without resorting to continuum approximations or homogenization, which enables us to compute families of stable multihump traveling-wave solutions with arbitrary wavelengths. We develop systematic semianalytical approaches for computing different families of nonlinear traveling waves parametrized by spatial periodicity (wave number) and energy, and show that in a certain asymptotic limit, these wave families converge to the known single-hump solitary wave studied by Nesterenko. In addition, we demonstrate the existence of an additional class of stable strongly localized out-of-phase standing waves in perfectly homogeneous granular chains with no precompression or disorder. Until now such localized solutions were known to exist only in granular chains with strong precompression. Our findings indicate that homogeneous granular chains possess complex intrinsic nonlinear dynamics, including intrinsic nonlinear energy transfer and localization phenomena.
| Original language | English (US) |
|---|---|
| Article number | 026603 |
| Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
| Volume | 82 |
| Issue number | 2 |
| DOIs | |
| State | Published - Aug 20 2010 |
Fingerprint
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics
Cite this
Traveling waves and localized modes in one-dimensional homogeneous granular chains with no precompression. / Starosvetsky, Yuli; Vakakis, Alexander F.
In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 82, No. 2, 026603, 20.08.2010.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Traveling waves and localized modes in one-dimensional homogeneous granular chains with no precompression
AU - Starosvetsky, Yuli
AU - Vakakis, Alexander F
PY - 2010/8/20
Y1 - 2010/8/20
N2 - We study a class of strongly nonlinear traveling waves and localized modes in one-dimensional homogeneous granular chains with no precompression. Until now the only traveling-wave solutions known for this class of systems were the single-hump solitary waves studied by Nesterenko in the continuum approximation limit. Instead, we directly study the discrete strongly nonlinear governing equations of motion of these media without resorting to continuum approximations or homogenization, which enables us to compute families of stable multihump traveling-wave solutions with arbitrary wavelengths. We develop systematic semianalytical approaches for computing different families of nonlinear traveling waves parametrized by spatial periodicity (wave number) and energy, and show that in a certain asymptotic limit, these wave families converge to the known single-hump solitary wave studied by Nesterenko. In addition, we demonstrate the existence of an additional class of stable strongly localized out-of-phase standing waves in perfectly homogeneous granular chains with no precompression or disorder. Until now such localized solutions were known to exist only in granular chains with strong precompression. Our findings indicate that homogeneous granular chains possess complex intrinsic nonlinear dynamics, including intrinsic nonlinear energy transfer and localization phenomena.
AB - We study a class of strongly nonlinear traveling waves and localized modes in one-dimensional homogeneous granular chains with no precompression. Until now the only traveling-wave solutions known for this class of systems were the single-hump solitary waves studied by Nesterenko in the continuum approximation limit. Instead, we directly study the discrete strongly nonlinear governing equations of motion of these media without resorting to continuum approximations or homogenization, which enables us to compute families of stable multihump traveling-wave solutions with arbitrary wavelengths. We develop systematic semianalytical approaches for computing different families of nonlinear traveling waves parametrized by spatial periodicity (wave number) and energy, and show that in a certain asymptotic limit, these wave families converge to the known single-hump solitary wave studied by Nesterenko. In addition, we demonstrate the existence of an additional class of stable strongly localized out-of-phase standing waves in perfectly homogeneous granular chains with no precompression or disorder. Until now such localized solutions were known to exist only in granular chains with strong precompression. Our findings indicate that homogeneous granular chains possess complex intrinsic nonlinear dynamics, including intrinsic nonlinear energy transfer and localization phenomena.
UR - http://www.scopus.com/inward/record.url?scp=77956117714&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77956117714&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.82.026603
DO - 10.1103/PhysRevE.82.026603
M3 - Article
AN - SCOPUS:77956117714
VL - 82
JO - Physical Review E
JF - Physical Review E
SN - 2470-0045
IS - 2
M1 - 026603
ER -