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Stochastic Model for Energy Propagation in Disordered Granular Chains.

Kianoosh Taghizadeh1,2, Rohit Kumar Shrivastava3, Stefan Luding1

  • 1Multi-Scale Mechanics, Faculty of Engineering Technology, MESA+, University of Twente, 7522NB Enschede, The Netherlands.

Materials (Basel, Switzerland)
|April 30, 2021
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Disordered granular chains show increased energy signal attenuation and localization with greater disorder. A new stochastic model simplifies energy propagation analysis for applications like non-destructive testing.

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Area of Science:

  • Physics
  • Mechanical Engineering
  • Materials Science

Background:

  • Mechanical wave propagation relies on energy and momentum transfer.
  • Disordered one-dimensional systems, like force-chains, exhibit complex wave behaviors.
  • Understanding energy transfer is crucial for analyzing wave propagation in granular media.

Purpose of the Study:

  • To analyze energy transfer in disordered one-dimensional granular systems.
  • To develop a simplified stochastic model for energy propagation.
  • To investigate the impact of disorder on wave attenuation and localization.

Main Methods:

  • Analytical solutions for deterministic Hertzian repulsive forces in pre-stressed random mass systems.
  • Review of pulse propagation phenomenology in disordered granular chains.
  • Development and calibration of a mean-field stochastic master equation model.

Main Results:

  • Increased disorder leads to higher attenuation and diffusive-like energy propagation.
  • Energy localization occurs at the source with increasing disorder.
  • Disorder transforms dispersive ballistic transport into low-pass filtering, localizing energy at lower masses.
  • The stochastic model accurately predicts energy propagation in wavenumber space.

Conclusions:

  • Disorder significantly impacts energy transfer dynamics in granular chains.
  • The proposed stochastic model offers a computationally efficient approach to analyze complex wave phenomena.
  • Findings have potential applications in non-destructive testing and resource exploration.