Nonlinear granular breathing

Abstract

A numerical study of the problem of driven horizontal alignments of solid, elastic spheres that are placed between two rigid walls is presented. The studies are confined to cases where the initial loading between the spheres is zero. The driving force is applied on the left outer sphere and directed into the chain. The spheres are considered to interact via the repulsive and strongly nonlinear Hertz potential. Three systems are analyzed, the monodispersed chain, the tapered chain and the decorated chain. A Hertzian chain over-compressed will respond via a dilation phase leading the system to a pulsatory mode which we call nonlinear breathing. Exhaustive studies show that the dynamics of monodispersed and tapered granular chains acted upon by a constant/time dependent force presents surprising features such as the breathing period (frequency) and the anomalous nonlinear resonance frequency. The breathing period characterizes the response of the system which is dependent upon the external force and is strongly influenced by the geometry of chain. Approximate relations for the breathing period and the anomalous nonlinear resonance frequency as functions of the magnitude of the driving force and of the chain's parameters are developed. Then the ratios of the analyzed quantities are compared to ratios obtained from simulations. Inertial mismatches introduced in granular chains enrich the dynamics of monodispersed chains leading to the discussion of continuing our work beyond this dissertation. Converting the ocean wave's energy and of small scale wind energy via granular chains into mechanical and electrical energies is discussed as possible application of the breathing phenomenon.