Nonlinear localization, passive wave arrest and traveling breathers in two-dimensional granular networks with discontinuous lateral boundary conditions

Abstract

We study nonlinear pulse propagation, breather formation and nonlinear localization leading to passive wave arrest in an impulsively forced two-dimensional granular network composed of two geometrically coupled ordered granular chains of spherical (heavy) beads with interstitial spherical (light) intruders, possessing discontinuous lateral boundary conditions. A striking feature of this network is that it completely lacks any linear acoustics, and, hence, it sustains zero speed of sound (as defined in classical acoustics). We show that this system possesses strongly nonlinear dynamics and acoustics that depend on the stiffness and mass ratios between the heavy beads and the light intruders. Moreover, polydispersity and nonlinearity within this granular network lead to complex phenomena, such as pulse propagation, motion localization, and formation of propagation and attenuation zones. In particular, depending on the design of this network the applied impulsive energy is either axially transmitted to its far field, or it is heavily scattered and localized close to the point of its generation by means of low-to-high energy transfers in its intrinsic dynamics. Such passive motion localization phenomena are due to nonlinear on-site potentials caused by the discontinuous lateral boundary conditions of the network, as well as to strongly nonlinear interactions between the heavy beads and the interstitial intruders, and, to the authors’ knowledge, are reported for the first time in the field of granular networks. These results demonstrate the high tunability of the nonlinear response of this system to energy and material properties.