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Overview of continuum and discrete modeling of a tapped column

We consider the behavior of a column of spheres that are subjected to a time-dependent external load in the form of vertical taps. Of interest are various dynamical properties, such as the motion of its mass center, its response to taps of different intensities and forms, and the effect of system size and material properties. The interplay between diverse time and length scales are the key contributors to the column’s evolving dynamics. Energy loss from collisional interactions takes place over the very short contact duration between spheres, while the column’s dilation and contraction occurs over a long time scale governed by the system features and tap intensity. Soft sphere discrete element simulations were conducted over a very wide parameter space to obtain a portrait of column behavior as embodied by the collective dynamics of the mass center motion. Results compared favorably with a derived reduced-order paradigm of the mass center motion (surprisingly analogous to that for a single bouncing ball on an oscillating plate) with respect to dynamical regimes and their transitions. A continuum model, obtained from a system of Newtonian equations, as a locally averaged limit in the transport mode along trajectories is derived, and a numerical solution protocol for a one-dimensional system is outlined. Typical trajectories and density evolution profiles are shown, which are compared with the predictions of new reduced dynamical models. We conclude with a discussion of our investigations to relate predictions of the continuum model with discrete simulations.

Author(s):

Anthony Rosato    
New Jersey Institute of Technology
United States

Denis Blackmore    
New Jersey Institute of Technology
United States

Hao Wu    
New Jersey Institute of Technology
United States

David Horntrop    
New Jersey Institute of Technology
United States

Luo Zuo    
New Jersey Institute of Technology
United States