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Updated: Aug 3, 2026
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Development of an Experimental Setup for the Measurement of the Coefficient of Restitution under Vacuum Conditions
Published on: March 29, 2016
Coefficient of restitution for one-dimensional harmonic solids
1Department of Math and Natural Sciences, D'Youville College, Buffalo, New York 14201-1084, USA.
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.
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.
- 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.
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