Strongly nonlinear spatially periodic traveling waves in granular dimer chains

K. R. Jayaprakash, Alexander F Vakakis, Yuli Starosvetsky

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In the present work we study the dynamics of spatially periodic traveling waves in granular 1:1 (each bead is followed and preceded by a bead of different mass and/or stiffness) dimer chain with no pre-compression. The dynamics of a 1:1 dimer chain is governed by a single parameter, the mass ratio of the two beads forming each dimer pair of the chain. In particular, we demonstrate numerically the formation of special families of traveling waves with spatially periodic waveforms that are realized in semi-infinite dimer chains with the application of an arbitrary impulse. These traveling waves were first observed in the form of oscillatory tails in the trail of the propagating primary pulse. The energy radiated by the propagating primary pulse manifests in the form of traveling waves of varying spatial periodicity depending on the mass ratio. These traveling waves depend only on the mass ratio and are rescalable with respect to any arbitrary applied energy. The dynamics of these families of traveling waves is systematically studied by considering finite dimer chains (termed the âreduced systemsâTM) subject to periodic boundary conditions. We demonstrate that these waves may exhibit interesting bifurcations or loss of stability as the system parameter varies. In turn, these bifurcations and stability exchanges in infinite dimer chains are correlated to previous studies of pulse attenuation in finite dimer chains through efficient energy radiation from the propagating pulse to the far field, mainly in the form of traveling waves. Based on these results a new formulation of attenuation and propagation zones (stop and pass bands) in semi-infinite granular dimer chains is proposed.

Original languageEnglish (US)
Title of host publicationASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012
Pages479-486
Number of pages8
EditionPARTS A AND B
DOIs
StatePublished - Dec 1 2012
EventASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012 - Chicago, IL, United States
Duration: Aug 12 2012Aug 12 2012

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
NumberPARTS A AND B
Volume1

Other

OtherASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012
CountryUnited States
CityChicago, IL
Period8/12/128/12/12

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ASJC Scopus subject areas

  • Modeling and Simulation
  • Mechanical Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design

Cite this

Jayaprakash, K. R., Vakakis, A. F., & Starosvetsky, Y. (2012). Strongly nonlinear spatially periodic traveling waves in granular dimer chains. In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012 (PARTS A AND B ed., pp. 479-486). (Proceedings of the ASME Design Engineering Technical Conference; Vol. 1, No. PARTS A AND B). https://doi.org/10.1115/DETC2012-70298