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The Nonlinear Dynamical and Shock Mitigation Properties of Tapered Chains

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Technical Report

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Army Research Laboratory Aberdeen Proving Ground United States

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An analytic and numerical study of the problem of mechanical impulse propagation through a horizontal alignment of progressively shrinking tapered elastic spheres that are placed between two rigid end walls is investigated. Particular attention is paid to the shock absorption and nonlinear dynamical properties as they pertain to energy partition. The studies are confined to cases where initial loading between the spheres is zero. The spheres are assumed to interact via the purely repulsive and strongly nonlinear Hertz potential.Propagation of energy is analytically studied in the hard-sphere approximation and parameter space diagrams plotting normalized kinetic energy of the smallest grain at the tapered end are developed for various chain lengths and tapering factors.These details are then compared to congruent diagrams obtained via extensive dynamical simulations. Our figures indicate that the ratios of the kinetic energies of the smallest to largest grains possess a gaussian dependence on tapering and an exponential decay when the number of grains increases. The results demonstrate the capability of these chains to thermalize propagating impulses and thereby act as potential shock absorbing devices.

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  • Mechanics

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