Article (Scientific journals)
Nonlinear normal modes and band zones in granular chains with no precompression
Jayaprakash, K.R.; Starosvetsky, Y.; Vakakis, A.F. et al.
2011In Nonlinear Dynamics, 63, p. 359-385
Peer reviewed
 

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Abstract :
[en] We study standing waves (nonlinear normal modes—NNMs) and band zones in finite granular chains composed of spherical granular beads in Hertzian contact, with fixed boundary conditions. Although these are homogeneous dynamical systems in the notation of Rosenberg, we show that the discontinuous nature of the dynamics leads to interesting effects such as separation between beads, NNMs that appear as traveling waves (these are characterized as pseudo-waves), and localization phenomena. In the limit of infinite extent, we study band zones, i.e., pass and stop bands in the frequency–energy plane of these dynamical systems, and classify the essentially nonlinear responses that occur in these bands. Moreover, we show how the topologies of these bands significantly affect the forced dynamics of these granular media subject to narrowband excitations. This work provides a classification of the coherent (regular) intrinsic dynamics of one-dimensional homogeneous granular chains with no pre-compression, and provides a rigorous theoretical foundation for further systematic study of the dynamics of granular systems, e.g., the effects of disorders or clearances, discrete breathers, nonlinear localized modes, and high-frequency scattering by local disorders. Moreover, it contributes toward the design of granular media as shock protectors, and in the passive mitigation of transmission of unwanted disturbances.
Disciplines :
Aerospace & aeronautics engineering
Author, co-author :
Jayaprakash, K.R.
Starosvetsky, Y.
Vakakis, A.F.
Peeters, Maxime 
Kerschen, Gaëtan  ;  Université de Liège - ULiège > Département d'aérospatiale et mécanique > Laboratoire de structures et systèmes spatiaux
Language :
English
Title :
Nonlinear normal modes and band zones in granular chains with no precompression
Publication date :
2011
Journal title :
Nonlinear Dynamics
ISSN :
0924-090X
eISSN :
1573-269X
Publisher :
Springer, Dordrecht, Netherlands
Volume :
63
Pages :
359-385
Peer reviewed :
Peer reviewed
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