Time-of-flight of solitary waves in dry and wet chains of beads: Experimental results and phenomenological models

Abstract

A highly nonlinear solitary wave is generated by impacting a dry chain of beads on one of its ends. Its speed depends on the speed v0 of the striker and the details of the contact force. The force on the bead at the site n = 7 and the end of the chain, as well as the time-of-flight (ToF) of both, the incident and reflected waves, is measured as a function of v0. This study was performed on a chain of stainless steel beads in two general cases: the dry chain and wet chains having three different types of oil on and around the contact points between the beads. The ToF displays a complex dependence on the fluid’s rheological properties not seen in previous studies. Power-law dependencies of the ToF on v0 in both, dry and wet, cases were found. It turned out that the Hertz plus viscoelastic interactions are not enough to account for the measured data. Two phenomenological models providing a unified and accurate account of our results were developed.