caa a22 4500 445360593 CHVBK 20180317142914.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s11071-010-9809-0 doi (NATIONALLICENCE)springer-10.1007/s11071-010-9809-0 Nonlinear normal modes and band zones in granular chains with no pre-compression [Elektronische Daten] [K. Jayaprakash, Yuli Starosvetsky, Alexander Vakakis, Maxime Peeters, Gaetan Kerschen] 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 (Adv. Appl. Mech. 9:155-242, 1966), 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. Springer Science+Business Media B.V., 2010 Nonlinear normal modes nationallicence Granular media nationallicence Band gaps nationallicence Jayaprakash K. Department of Mechanical Science and Engineering, University of Illinois at Urbana Champaign, 1206 W. Green Street, 61822, Urbana, IL, USA aut Starosvetsky Yuli Department of Mechanical Science and Engineering, University of Illinois at Urbana Champaign, 1206 W. Green Street, 61822, Urbana, IL, USA aut Vakakis Alexander Department of Mechanical Science and Engineering, University of Illinois at Urbana Champaign, 1206 W. Green Street, 61822, Urbana, IL, USA aut Peeters Maxime Department of Aerospace and Mechanical Engineering, University of Liege, 1, Chemin des Chevreuils (B52/3), 4000, Liege, Belgium aut Kerschen Gaetan Department of Aerospace and Mechanical Engineering, University of Liege, 1, Chemin des Chevreuils (B52/3), 4000, Liege, Belgium aut Nonlinear Dynamics Springer Netherlands 63/3(2011-02-01), 359-385 0924-090X 63:3<359 2011 63 11071 https://doi.org/10.1007/s11071-010-9809-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-010-9809-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jayaprakash K. Department of Mechanical Science and Engineering, University of Illinois at Urbana Champaign, 1206 W. Green Street, 61822, Urbana, IL, USA aut NATIONALLICENCE 700 1- Starosvetsky Yuli Department of Mechanical Science and Engineering, University of Illinois at Urbana Champaign, 1206 W. Green Street, 61822, Urbana, IL, USA aut NATIONALLICENCE 700 1- Vakakis Alexander Department of Mechanical Science and Engineering, University of Illinois at Urbana Champaign, 1206 W. Green Street, 61822, Urbana, IL, USA aut NATIONALLICENCE 700 1- Peeters Maxime Department of Aerospace and Mechanical Engineering, University of Liege, 1, Chemin des Chevreuils (B52/3), 4000, Liege, Belgium aut NATIONALLICENCE 700 1- Kerschen Gaetan Department of Aerospace and Mechanical Engineering, University of Liege, 1, Chemin des Chevreuils (B52/3), 4000, Liege, Belgium aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 63/3(2011-02-01), 359-385 0924-090X 63:3<359 2011 63 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer