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Scattering of waves by impurities in precompressed granular chains
Alejandro J Martínez1, Hiromi Yasuda2, Eunho Kim2,3
1Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK.
Physical Review. E
|June 15, 2016
Summary
We discovered a quantum physics-like resonance in granular chains, enabling full wave transmission through impurities. This Ramsauer-Townsend (RT) resonance can be tuned and even create reflectionless modes in disordered chains.
Area of Science:
- Physics
- Materials Science
- Acoustics
Background:
- Granular chains exhibit unique wave propagation properties.
- Impurities can disrupt or modify wave transmission.
- Precompression significantly alters the behavior of granular materials.
Purpose of the Study:
- To investigate wave scattering by impurities in precompressed granular chains.
- To derive analytical expressions for wave reflection and transmission.
- To explore the phenomenon of resonance in such systems.
Main Methods:
- Linear scattering theory for plane waves.
- Derivation of closed-form expressions for scattering coefficients.
- Numerical simulations and experimental validation.
- Analysis of single and double impurity configurations.
Main Results:
- Identified frequency-dependent wave attenuation and transmission in single-impurity chains.
- Discovered a Ramsauer-Townsend (RT) resonance in double-impurity chains enabling full transmission.
- Demonstrated tunability of the RT resonance frequency within the host chain's passband.
- Observed near-complete transmission at RT resonance frequencies experimentally.
- Showcased RT resonance's potential for creating reflectionless modes.
Conclusions:
- Strongly precompressed granular chains exhibit tunable wave scattering properties.
- The Ramsauer-Townsend resonance offers a mechanism for complete wave transmission through impurities.
- This phenomenon has implications for designing advanced acoustic or mechanical filters and metamaterials.
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