Extreme control of impulse transmission by cylinder-based nonlinear phononic crystals

Abstract

We present a novel device that can offer two extremes of elastic wave propagation --- nearly complete transmission and strong attenuation under impulse excitation. The mechanism of this highly tunable device relies on intermixing effects of dispersion and nonlinearity. The device consists of identical cylinders arranged in a chain, which interact with each other as per nonlinear Hertz's contact law. For a `dimer' configuration, i.e., two different contact angles alternating in the chain, we analytically, numerically, and experimentally show that impulse excitation can either propagate as a localized wave, or it can travel as a highly dispersive wave. Remarkably, these extremes can be achieved in this periodic arrangement simply by \textit{in-situ} control of contact angles between cylinders. We close the discussion by highlighting the key characteristics of the mechanisms that facilitate strong attenuation of incident impulse. These include low frequency to high frequency (LF-HF) scattering, and turbulence-like cascading in a periodic system. We thus envision that these adaptive, cylinder-based nonlinear phononic crystals, in conjunction with conventional impact mitigation mechanisms, could be used to design highly tunable and efficient impact manipulation devices.