Scattering of Solitary Waves and Excitation of Transient Breathers in Granular Media by Light Intruders and No Precompression

Abstract

We analyze the dynamics of strongly nonlinear granular chains of beads in Hertzian contact with light intruders. We show that the interactions of the light intruders with solitary pulses propagating through the granular medium can be approximately studied by reduced models of the intruders with only their neighboring beads under similar excitation conditions. Studying the reduced models, we identify weakly and strongly nonlinear regimes in the dynamics, depending on the degree of compression between beads and on the occurrence of separation between neighboring beads leading to collisions. We analyze weakly and strongly nonlinear oscillatory regimes of the intruder dynamics by multiple-scale analysis, and by applying special nonsmooth coordinate transformations. When separation between beads occurs, localized transient breathers are excited, corresponding to repeated collisions of an intruder with its neighbors. This leads to high-frequency scattering energy, and to radiation of energy in the granular medium in the form of low-amplitude slowly modulated oscillatory pulses. We find that repeated excitation of localized transient breathers by an array of periodically placed intruders can result in drastic reduction of the amplitude of a solitary wave propagating through the granular medium. This indicates that this type of granular media can be designed as effective shock attenuators.