Wave localization in strongly nonlinear Hertzian chains with mass defect

Stéphane Job (1, 2) , Francisco Santibanez , Franco Tapia , Francisco Melo

1 LISMMA - Laboratoire d'Ingénierie des Systèmes Mécaniques et des MAtériaux
2 SUPMECA - SUPMECA - Institut supérieur de mécanique de Paris

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.

Domaines: Science des matériaux [cond-mat.mtrl-sci]

Stéphane Job, Francisco Santibanez, Franco Tapia, Francisco Melo. Wave localization in strongly nonlinear Hertzian chains with mass defect. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2009, 80 (2), pp.025602(R). ⟨10.1103/PhysRevE.80.025602⟩. ⟨hal-00624740⟩