Traveling waves in trimer granular lattice I: Bifurcation structure of traveling waves in the unit-cell model

Jayaprakash, KR and Shiffer, A and Starosvetsky, Y (2016) Traveling waves in trimer granular lattice I: Bifurcation structure of traveling waves in the unit-cell model. In: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 38 . pp. 8-22.

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Abstract

Present paper is the first one in the series devoted to the dynamics of traveling waves emerging in the uncompressed, tri-atomic granular crystals. This work is primarily concerned with the dynamics of one-dimensional periodic granular trimer (tri-atomic) chains in the state of acoustic vacuum. Each unit cell consists of three spherical particles of different masses subject to periodic boundary conditions. Hertzian interaction law governs the mutual interaction of these particles. Under the assumption of zero pre-compression, this interaction is modeled as purely nonlinear, which means the absence of linear force component. The dynamics of such chains is governed by the two system parameters that scale the mass ratios between the particles of the unit cell. Such a system supports two different classes of periodic solutions namely the traveling and standing waves. The primary objective of the present study is the numerical analysis of the bifurcation structure of these solutions with emphasis on the dynamics of traveling waves. In fact, understanding of the bifurcation structure of the traveling wave solutions emerging in the unit-cell granular trimer is rather important and can shed light on the more complex nonlinear wave phenomena emerging in semi-infinite trimer chains. (c) 2016 Elsevier B.V. All rights reserved.

Item Type:	Journal Article
Publication:	COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Publisher:	ELSEVIER SCIENCE BV
Additional Information:	Copy right for this article belongs to the ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM,NETHERLANDS
Keywords:	Nonlinear normal modes; Traveling waves; Granular trimers; Bifurcations
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	12 May 2016 05:43
Last Modified:	12 May 2016 05:43
URI:	http://eprints.iisc.ac.in/id/eprint/53800

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