Primary pulse transmission in coupled steel granular chains embedded in PDMS matrix: Experiment and modeling

M. Arif Hasan, Shinhu Cho, Kevin Remick, Alexander F Vakakis, D. Michael McFarland, Waltraud M Kriven

Research output: Contribution to journalArticle

Abstract

We present an experimental study of primary pulse transmission in coupled ordered steel granular chains embedded in poly-di-methyl-siloxane (PDMS) elastic matrix. Two granular one-dimensional chains are considered (an 'excited' and an 'absorbing' one), each composed of 11 identical steel beads of 9.5 mm diameter with the centerline of the chain spaced at fixed distances of 0.5, 1.5 or 2.5 mm apart. We directly force one of the chains (the excited one) by a transient pulse and measure, by means of laser vibrometry, the primary transmitted pulses at the end beads of both chains and at the first bead of the absorbing chain. It is well known that the dynamics of this type of ordered granular media is strongly nonlinear due, (i) to Hertzian interactions between adjacent beads, and (ii) to possible bead separations in the absence of compressive forces and ensuing collisions between neighboring beads. Accordingly, we develop a strongly nonlinear theoretical model that takes into account the coupling of the granular chains due to the PDMS matrix, with the aim to model primary pulse transmission in this system. After validating the model with experimental measurements, we employ it in a predictive fashion to estimate energy transfer between chains as a function of the interspatial distance between chains. Furthermore, based on this model we perform predictive matrix design to achieve maximum energy transfer from the excited to the absorbing chain, and provide a theoretical explanation of the nonlinear dynamics governing energy transfer (including energy equi-partition) in this system.

Original languageEnglish (US)
Pages (from-to)3207-3224
Number of pages18
JournalInternational Journal of Solids and Structures
Volume50
Issue number20-21
DOIs
StatePublished - Oct 1 2013

Fingerprint

Siloxanes
Steel
siloxanes
steels
Energy transfer
beads
matrices
pulses
Modeling
Experiment
Laser pulses
Experiments
Energy Transfer
Absorbing
energy transfer
Lasers
equipartition theorem
Equipartition
Granular Media
Theoretical Model

Keywords

  • Elastic matrix
  • Energy transfers
  • Granular chains
  • Primary pulse transmission

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

Primary pulse transmission in coupled steel granular chains embedded in PDMS matrix : Experiment and modeling. / Hasan, M. Arif; Cho, Shinhu; Remick, Kevin; Vakakis, Alexander F; McFarland, D. Michael; Kriven, Waltraud M.

In: International Journal of Solids and Structures, Vol. 50, No. 20-21, 01.10.2013, p. 3207-3224.

Research output: Contribution to journalArticle

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AB - We present an experimental study of primary pulse transmission in coupled ordered steel granular chains embedded in poly-di-methyl-siloxane (PDMS) elastic matrix. Two granular one-dimensional chains are considered (an 'excited' and an 'absorbing' one), each composed of 11 identical steel beads of 9.5 mm diameter with the centerline of the chain spaced at fixed distances of 0.5, 1.5 or 2.5 mm apart. We directly force one of the chains (the excited one) by a transient pulse and measure, by means of laser vibrometry, the primary transmitted pulses at the end beads of both chains and at the first bead of the absorbing chain. It is well known that the dynamics of this type of ordered granular media is strongly nonlinear due, (i) to Hertzian interactions between adjacent beads, and (ii) to possible bead separations in the absence of compressive forces and ensuing collisions between neighboring beads. Accordingly, we develop a strongly nonlinear theoretical model that takes into account the coupling of the granular chains due to the PDMS matrix, with the aim to model primary pulse transmission in this system. After validating the model with experimental measurements, we employ it in a predictive fashion to estimate energy transfer between chains as a function of the interspatial distance between chains. Furthermore, based on this model we perform predictive matrix design to achieve maximum energy transfer from the excited to the absorbing chain, and provide a theoretical explanation of the nonlinear dynamics governing energy transfer (including energy equi-partition) in this system.

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