A ONE-DIMENSIONAL MODEL FOR THE TRANSITION FROM PERIODIC TO CHAOTIC MOTIONS IN GRANULAR SHEAR FLOWS

A simple one-dimensional mechanical model to simulate some aspects of the dynamics of granular flow is suggested. The model consists of a vi sco-elastic packet bouncing between two oscillating walls. The motion of the walls is prescribed to be harmonic. The amplitude and frequency of the wall motion are related to the concentration and shear rate, r espectively. The dynamics of the system is studied for various paramet er combinations and it is shown that periodic as well as chaotic motio ns are possible for different parameters and initial conditions. Resul ts are presented in the form of time histories, power spectral densiti es, phase diagrams, Poincare plots and bifurcation diagrams. This simp le one-dimensional model presents many features that are analogous to those observed in the two-dimensional simple shear flow of disks.