Nonlinear Low-to-High Frequency Energy Cascades in Diatomic Granular Crystals

Abstract

We study wave propagation in strongly nonlinear 1D diatomic granular crystals under an impact load. Depending on the mass ratio of the `light' to `heavy' beads, this system exhibits rich wave dynamics from highly localized traveling waves to highly dispersive waves featuring strong attenuation. We experimentally demonstrate the nonlinear resonant and anti-resonant interactions of particles and verify that the nonlinear resonance results in strong wave attenuation, leading to highly efficient nonlinear energy cascading without relying on material damping. In this process, mechanical energy is transferred from low to high frequencies, while propagating waves emerge in both ordered and chaotic waveforms via a distinctive spatial cascading. This energy transfer mechanism from lower to higher frequencies and wavenumbers is of particular significance towards the design of novel nonlinear acoustic metamaterials with inherently passive energy redistribution properties.