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

TL;DR

This paper develops a conformal gradient index phononic crystal theory for elastic wave focusing in curved structures, validated through simulations and experiments on a steel pipe and a 3D-printed conical lens.

Contribution

It introduces a novel theoretical framework for designing GRIN-PC lenses on non-planar structures, expanding their application scope.

Findings

Accurately predicts wave focusing in curved structures.

Validates theoretical predictions with numerical simulations.

Demonstrates elastic wave focusing with experimental validation.

Abstract

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.