Conformal Gradient Index Phononic Crystal Lenses: Theory and Application on Non-planar Structures

The gradient index phononic crystal (GRIN-PC) lens concept has been proven very effective for focusing elastic waves at a desired location. Although well-studied for planar structures, GRIN-PC lenses for elastic wave focusing in curved structures are scarce and lack the theoretical framework for studying the wave focusing mechanism. In this work, we develop conformal GRIN-PC theory to analyze wave focusing in non-planar geometries and present a design framework for conformal GRIN-PC lenses to be implemented over curved structures. The proposed conformal GRIN-PC theory studies the wave propagation in a curved GRIN-PC lens using ray trajectories that meet at the focal spot of the lens. We apply the conformal GRIN-PC theory to accurately predict the focal region of the GRIN-PC lens implemented over a steel pipe and validate the results with numerical simulations. Further, the design framework is utilized to design a 3D-printed conical GRIN-PC lens. The elastic wave focusing in the conical lens is demonstrated using numerical simulations and is further validated with experiments.