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Coefficient of restitution for one-dimensional harmonic solids

Basile1, Dumont

  • 1Department of Math and Natural Sciences, D'Youville College, Buffalo, New York 14201-1084, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 25, 2000
PubMed
Summary

In collisions with a hard wall, homogeneous harmonic solids perfectly rebound (eta=1). Introducing weaker springs reduces restitution, with energy shifting to low-frequency modes.

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Area of Science:

  • Solid Mechanics
  • Statistical Physics
  • Materials Science

Background:

  • The coefficient of restitution (eta) quantifies energy loss during collisions.
  • Understanding energy dissipation in solids is crucial for material design and performance.
  • Previous studies often focused on simplified models or specific material types.

Purpose of the Study:

  • To investigate the coefficient of restitution (eta) for one-dimensional harmonic solids colliding with hard and soft walls.
  • To analyze the influence of internal spring variations on energy dissipation during impact.
  • To explore the redistribution of energy among normal modes post-collision.

Main Methods:

  • Numerical algorithm based on the time evolution of normal modes.
  • Calculation of the coefficient of restitution (eta) for homogeneous and non-homogeneous chains.

Related Experiment Videos

  • Perturbation theory applied to collisions with a soft wall.

    • Main Results:

    • For homogeneous chains colliding with a hard wall, eta approaches 1 in the thermodynamic limit.
    • Chains with weaker springs in the front half exhibit eta < 1, with energy transferring to low-frequency normal modes.
    • Collisions with a soft wall show eta = 1 in the extreme soft limit, but inelasticity increases with chain size.

    Conclusions:

    • The internal structure of a harmonic solid significantly impacts its coefficient of restitution during hard wall collisions.
    • Energy dissipation mechanisms differ between hard and soft wall impacts, particularly concerning the role of normal modes.
    • These findings offer insights into the fundamental physics of impact and energy transfer in one-dimensional systems.