Non-cascade frequency-mixing processes for elastic waves in unconsolidated granular materials.

Due to disorder, contacts between beads in stressed granular assemblages are not equally loaded. There exists a distribution of contact static loads, containing weakly loaded contacts (the weak contacts) and strongly loaded contacts (the strong contacts involved in the so-called force chains). For an elastic periodic excitation with a given deformation amplitude, the weakest contacts are supposed to clap (periodically open and close) due to the action of the acoustic wave. When increasing the acoustic amplitude, more and more contacts are clapping, progressively producing a non classical spectral signature. Presented spectra have been observed in a laboratory scale experiment, where two frequencies were initially launched in the medium. Results are obtained for increasing pump wave amplitudes and different frequency pairs. These experimental results are in good agreement with a model derived from the Hertz theory of contacts with possibility of clapping.