Wave localization in strongly nonlinear Hertzian chains with mass defect

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.

4 pages, 5 figures, submitted for publication

References in corpus (4)

• Energy trapping and shock disintegration in a composite granular medium
• How Hertzian solitary waves interact with boundaries in a 1-D granular medium
• Solitary wave trains in granular chains: Experiments, theory and simulations
• Experimental evidence of shock mitigation in a Hertzian tapered chain

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