Wave localization in strongly nonlinear Hertzian chains with mass defect

TL;DR

This paper studies how a mass defect in a nonlinear Hertzian chain causes localized oscillations when interacting with solitary waves, revealing nonlinear frequency dependence and amplitude enhancement due to gap formation.

Contribution

It provides experimental and numerical evidence of localized modes caused by mass defects in nonlinear chains, with a focus on frequency and amplitude behaviors.

Findings

Localized oscillations occur when solitary waves interact with a mass defect.

Oscillation frequency exceeds the incident wave spectrum and depends nonlinearly on defect size and wave strength.

Gaps opening between grains amplify oscillation amplitudes.

Abstract

We investigate the dynamical response of a mass defect in a one-dimensional non-loaded horizontal chain of identical spheres which interact via the nonlinear Hertz potential. Our experiments show that the interaction of a solitary wave with a light intruder excites localized mode. In agreement with dimensional analysis, we find that the frequency of localized oscillations exceeds the incident wave frequency spectrum and nonlinearly depends on the size of the intruder and on the incident wave strength. The absence of tensile stress between grains allows some gaps to open, which in turn induce a significant enhancement of the oscillations amplitude. We performed numerical simulations that precisely describe our observations without any adjusting parameters.