Design of patch-shaped lens with thickness variations for elastic wave focusing in thin-plate structures

Abstract

In mechanical engineering, focusing on elastic waves is pivotal for applications, such as energy harvesting, shock mitigation, and wave manipulation. While phononic crystals have historically been a key method for managing wave propagation, this study explores a novel technique. This method introduces gradient refractive-index (GRIN) lenses by altering the plate thickness and creating localized high-refractive-index zones. Unlike traditional methods, this localized GRIN approach aims to overcome the fabrication and structural limitations, particularly in thin structures. The patch-shaped lenses offer the potential for elastic wave focusing in thinner structures without any degradation of structural performance. Through numerical analysis, we established design principles and examined the elastic wave propagation and focusing characteristics across various thickness variation profiles. This study conducts a thorough analytical and experimental evaluation of these lenses to confirm their effectiveness, structural robustness, and suitability for optimizing wave concentration in various mechanical engineering applications. The research represents an alternative, innovative, and promising pathway in the field of wave focusing, transcending the traditional constraints of thin plate structures.