Date of Award

Spring 2014

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mechanical Engineering - (Ph.D.)

Department

Mechanical and Industrial Engineering

First Advisor

Anthony D. Rosato

Second Advisor

Pushpendra Singh

Third Advisor

I. Joga Rao

Fourth Advisor

Ian Sanford Fischer

Fifth Advisor

David James Horntrop

Sixth Advisor

Denis L. Blackmore

Abstract

This dissertation is focused on a discrete element study of the dynamics of a one- dimensional column of inelastic spheres that it subjected to taps by prescribing a half sine wave pulse to supporting floor. Contact interactions obey the Walton-Braun soft-sphere model in which the loading (unloading) path is governing by linear springs of stiffness K1, thereby producing col lisional energy loss through a constant restitution coefficient e. Over a ‘short time scale’, computations are done to examine the floor pulse wave as it propagates through the column contact network. Comparisons of the simulated findings are made with experimental measurements in the literature where possible. Principal emphasis is placed on computing various measures of the evolution of the system that occurs over a long time scale, i.e., the time interval over which the system undergoes a dilation and contraction to a quiescent state after the application of the tap. Here the goal is to chart the column behavior as a function of the amplitude and frequency of the tap, as well as the number of particles in the system and energy dissipation as characterized by. While at the outset, it may appear that this is a simple system, the dynamics in fact are enormously complex as computed Poincaré maps of the mass center trajectories reveal periodic, period doubling and chaotic regimes.

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