Granular Crystals: Controlling Mechanical Energy with Nonlinearity and Discreteness

Abstract

The presence of structural discreteness and periodicity can affect the propagation of phonons, sound, and other mechanical waves. A fundamental property of many of the periodic structures and materials designed for this purpose is the presence of complete band gaps in their dispersion relation. Waves with frequencies in the band gap cannot propagate and are reflected by the material. Like the concept of a band gap, the functionality of these periodic structures has historically been based on concepts from linear dynamics. Nonlinear systems can offer increased flexibility over linear systems including new ways to localize energy, convert energy between frequencies, and tune the response of the system. Granular crystals are arrays of elastic particles that interact nonlinearly via Hertzian contact, and are a type of nonlinear periodic structure whose response to dynamic excitations can be tuned to encompass linear, weakly nonlinear, and strongly nonlinear regimes. Drawing on ideas from condensed matter physics and nonlinear science, this thesis focuses on how the nonlinearity and structural discreteness of granular crystals can be used to control mechanical energy. The dynamic response of one-dimensional granular crystals composed of compressed elastic spheres (or cylinders) is studied using a combination of experimental, numerical, and analytical techniques. The discovery of fundamental physical phenomena occurring in the linear and weakly nonlinear regimes is described, along with how such phenomena can be used to create new ways to control the propagation of mechanical wave energy. The specific mechanisms investigated include tunable frequency band gaps, discrete breathers, nonlinear localized defect modes, and bifurcations. These mechanisms are utilized to create novel devices for tunable vibration filtering, energy harvesting and conversion, and tunable acoustic rectification.