Scattering of waves by impurities in precompressed granular chains.
We study scattering of waves by impurities in strongly precompressed granular chains. We explore the linear scattering of plane waves and identify a closed-form expression for the reflection and transmission coefficients for the scattering of the waves from both a single impurity and a double impurity. For single-impurity chains, we show that, within the transmission band of the host granular chain, high-frequency waves are strongly attenuated (such that the transmission coefficient vanishes as the wavenumber k→±π), whereas low-frequency waves are well-transmitted through the impurity. For double-impurity chains, we identify a resonance-enabling full transmission at a particular frequency-in a manner that is analogous to the Ramsauer-Townsend (RT) resonance from quantum physics. We also demonstrate that one can tune the frequency of the RT resonance to any value in the pass band of the host chain. We corroborate our theoretical predictions both numerically and experimentally, and we directly observe almost complete transmission for frequencies close to the RT resonance frequency. Finally, we show how this RT resonance can lead to the existence of reflectionless modes in granular chains (including disordered ones) with multiple double impurities.
Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK.
Alejandro J
AJ
Martínez
Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195-2400, USA.
Hiromi
H
Yasuda
Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195-2400, USA.|Division of Mechanical System Engineering, Automotive Hi-Technology Research Center, Chonbuk National University, 567 Baeje-daero, Deokjin-gu, Jeonju-si, Jeollabuk-do 54896, Republic of Korea.
Eunho
E
Kim
Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA.|Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.
P G
PG
Kevrekidis
Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK.|CABDyN Complexity Centre, University of Oxford, Oxford OX1 1HP, UK.
Mason A
MA
Porter
Aeronautics and Astronautics, University of Washington, Seattle, Washington 98195-2400, USA.
Jinkyu
J
Yang