Thesis (Ph.D.)--University of Washington, 2018Lattice structures have been studied for a long time but have come into spotlight in recent years as a test bed for various wave manipulations. Researchers have started to pay attention not only to their interesting static/dynamic behaviors but also to their high tunability. In this work, we explore linear and nonlinear elastic wave dynamics in lattice chains. Specifically, the chains are composed of 3D-printed hollow elliptical cylinders (HECs). 3D-printing provides us the freedom of altering the design of the HECs, hence offering high tunability of the HEC lattice chains. This implies that we can assemble different systems for various wave manipulations. First, we investigate shock wave propagation in the homogeneous chain. We experimentally and numerically demonstrate the formation of dispersive rarefaction shocks in the 3D-printed soft HEC chain. We claim that the dispersion in the wave tails and the rarefaction in the leading pulse of the dispersive rarefaction shocks provide innate advantage in energy absorption. Next, we consider graded chains made of HECs with varying thicknesses, where asymmetric wave dynamics is invoked. In the decreasing thickness chain, we find out that elastic waves are trapped at a specific location of the chain, which is based on the principle of the Bloch oscillations. This trapping mechanism depends on the input frequency of the propagating elastic waves. In the increasing thickness chain, however, we observe waves are reflected back in the middle of the chain whose location depends on the input frequency. Finally, we show asymmetric nonlinear wave dynamics in the graded HEC chain. Under the same striker impact, the wave decelerates in the decreasing thickness chain whereas it accelerates in the increasing thickness chain. We discover that there is near an order-of-magnitude difference in transmitted force between these two directions. We extend our findings from the 1D systems to a 2D lattice, with a possibility of using it as a core material in sandwich structures. These results suggest that the 3D-printed HECs can be built into different structures to manipulate mechanical waves in various ways, such as attenuation, localization, and filtering. We can exploit the findings in this work for potential applications in impact mitigation, vibration isolation, and energy harvesting
