Nonlinear Resonances Leading to Strong Pulse Attenuation in Granular Dimer Chains

Introduction

“…The absence of pre-compression can reveal exciting new solutions, like families of solitary waves [101] which are analogs to those realized in the homogeneous granular chains, and the traveling waves [102,103]. Further to that, the resonance phenomena that lead to a substantial attenuation of the propagating pulses were explored [94]. Moreover, the phenomena of the resonances and the anti-resonances have been experimentally verified by Potekin et al [104].…”

“…In the previous studies of tapered chains or dimers [94,107], the applied shocks attenuate as they propagate through these granular chains. Another methodology evolved for the same application of the shock protection/isolation is by entrapping/containing the shock energy in a certain spatial domain of the chain.…”

“…Polydisperse systems typically support waves that radiate energy to the far field as they travel, which distorts their initial waveforms due to the continuous energy 'leakage'. In the context of the one-dimensional granular media much emphasis has been on periodic dimer systems [48,[91][92][93][94][95][96], i.e., the systems composed of pairs of dissimilar beads, more often called 1: 1 dimers. The dynamics of these systems has been studied both theoretically in the continuum approximation [97] and experimentally [92,93,97].…”

“…Hence, we claim that to investigate the dynamics of the granular dimer chains the discrete approach is more suitable, unless the granular chain is pre-compressed and bead separation is suppressed. In this context, the frequency band gaps in pre-compressed dimer chains have been explored by Herbold et al [94], whereas discrete breathers in these systems have been studied by Boechler et al [95]. Further to that, intrinsic energy localization by exciting breathers in the dimer chains has been studied by Theocharis et al [100].…”

Mechanical wave propagation within nanogold granular crystals

“…For example, in compressed diatomic chains of alternating steel and aluminum spherical granules, the existence of discrete breathers was theoretically and experimentally proved, where sustained, exponentially localized oscillations emerge at a frequency inside the forbidden band of the linear Fourier spectrum 31 . For uncompressed diatomic lattices assembled by two different masses, strongly nonlinear resonances and anti-resonances are described by theory and experiments, resulting in 4 an optimal wave attenuation and a new type of solitary wave respectively [32][33][34] .…”