Publication Date

January 2016

Journal or Book Title

Physical Review E

Abstract

We study scattering of waves by impurities in strongly precompressed granular chains. We ex-plore the linear scattering of plane waves and identify a closed-form expression for the reectionand transmission coecients for the scattering of the waves from both a single impurity and a dou-ble impurity. For single-impurity chains, we show that, within the transmission band of the hostgranular chain, high-frequency waves are strongly attenuated (such that the transmission coecientvanishes as the wavenumber k ! ), whereas low-frequency waves are well-transmitted throughthe impurity. For double-impurity chains, we identify a resonance | enabling full transmission at aparticular frequency | in a manner that is analogous to the Ramsauer{Townsend (RT) resonancefrom quantum physics. We also demonstrate that one can tune the frequency of the RT resonanceto any value in the pass band of the host chain. We corroborate our theoretical predictions bothnumerically and experimentally, and we directly observe complete transmission for frequencies closeto the RT resonance frequency. Finally, we show how this RT resonance can lead to the existenceof reectionless modes even in granular chains (including disordered ones) with multiple doubleimpurities.

Volume

93

Included in

Mathematics Commons

Share

COinS