Propagating discrete breathers in forced one-dimensional granular networks: theory and experiment

摘要

We study propagating discrete breathers in forced one-dimensional nonlinear granular media on linear elastic foundations, with no pre-compression. These are modulated oscillatory travelling wavepackets that are formed due to the dynamical balance between the strongly nonlinear Hertzian interactions between the beads of the granular chain, the dispersion caused by the on-site elastic potential, and the intrinsic discreteness of the medium. In the theoretical part of this study we consider granular chains with and without dissipative terms. We analytically prove the existence of breathers in harmonically forced granular chains governed by nonlinear combination resonances in the forced dynamics. Our analytical models predict the speed and frequency contents of the discrete breathers which are validated by direct computational results. We show the existence of countable infinities of breathers in these systems corresponding to higher-order resonances between the applied harmonic excitations and the intrinsic frequency components of the modulated wavepackets. These families are energy-dependent and tunable with the harmonic excitation. Finally, we experimentally validate the theoretical results with a fixture that is designed to realize robustly the predicted propagating breathers. Considering impulsive excitations we experimentally verify the energy tunability of the breathers, and compare the experimental results to computational reconstructions of the results. These findings pave the way for designing granular chains for predictable and focused energy transmission.