Subharmonics and noise excitation in transmission of acoustic wave through unconsolidated granular medium

Abstract

First laboratory-scale experimental observation of both subharmonics excitation and significant increase in noise level caused by propagation of the acoustic wave in unconsolidated granular material is reported. The bifurcation phenomenon, taking place above a critical level of acoustic excitation (and opening the subharmonics route to chaos) is attributed to the interaction of acoustic wave with distributed system of highly nonlinear inter-grain contacts. The estimates demonstrated that these are weak contacts (loaded at least two orders of magnitude weaker than in average) that might be responsible for the observed nonlinear effects. The additional intermittent contacts created by the acoustic wave (which are open in the absence of acoustic loading) can also contribute. In the clapping (tapping) regime, each of these contacts individually is similar to an impact oscillator, for which the scenario of period doubling cascade and the transition to chaotic behavior has been predicted theoretically and observed experimentally earlier. The experiments confirm that the nonlinear interactions of acoustic waves in granular assemblages are highly sensitive to the fraction of weakly loaded (and unloaded) contacts, information on which is difficult to access by any other experimental methods.