Role of Phononic Crystals in Elastic Wave Focusing, Guiding, and Sensing Applications

Abstract

Mechanical waves enable energy transport through the oscillation or vibration of particles within their propagation medium. They are essential in many applications that impact our daily lives and various fields, including medical diagnostics, structural health monitoring, communication, and seismic exploration. Hence, their understanding and manipulation are important for technological advancements and scientific discoveries. Artificially engineered periodic composite structures, called phononic crystals (PCs), have the ability to manipulate acoustic and elastic waves through the formation of Bragg bandgaps. Bragg bandgaps further lead to wave dispersion, band folding, and in-gap defect and topological modes that offer exceptional wave control. Unlike acoustic waves, elastic waves exhibit intricate behaviors due to the presence of additional transverse polarization, which makes their exploration using PCs a promising avenue for further scientific exploration. This thesis explores the role of PCs in elastic wave focusing, guiding, and sensing, offering insights into the potential for advanced wave applications.

Elastic wave focusing enhances the efficacy of engineering applications, such as non-destructive testing, by mitigating losses caused by wave attenuation. Phononic crystals facilitate wave focusing through the use of gradient-index (GRIN) and negative-index lenses. Wave focusing is achieved by manipulating the refractive index distribution in GRIN-PCs and via negative refraction in negative-index lenses. The current state-of-the-art primarily features planar GRIN-PC lenses. To this end, this thesis introduces a conformal GRIN-PC theory for elastic wave-focusing on curved structures. Utilizing this theory, non-planar GRIN-PC lenses are designed to demonstrate wave focusing in cylindrical and conical shells. Additionally, negative refraction offers higher focusing resolution compared to positive-index lenses, such as GRIN-PCs. However, negative-index PC lenses are narrowband and are less explored in the context of elastic waves. This research enables subwavelength focusing of flexural elastic waves in plates using negative-index PC lenses. The anisotropy of square lattice PC is harnessed for the broadband operation of the lens, while the focusing resolution is enhanced by leveraging bound phonon mode for evanescent wave amplification.

Another way of wave localization in PCs is via the defect and topological modes. The thesis explores the defect modes in PC plates for liquid property sensing using guided elastic waves for a more compact design alternative to their acoustic counterparts. Defect modes are located within the bandgaps of PCs at a specific frequency, making them easier to detect using transmission analysis. In the PC, a liquid sample is introduced as a defect, and the defect frequency is calibrated to the changes in the acoustic properties of the liquid; thus, providing a platform for sensing liquid properties. Moreover, topological modes are robust to disorder and imperfections due to topological protection. This thesis investigates the topological mechanics of twisted kagome lattices protected by duality symmetry. We found peculiar topological modes in self-dual twisted kagome lattice that facilitate robust wave localization, and tunable and reconfigurable waveguiding.

In summary, this research uncovers novel concepts for elastic wave manipulation using PCs. Elastic wave focusing would enable long-distance information transfer in structural health monitoring of curved structures, such as pipelines. Further, negative-index lenses would yield high resolution for better visualization of internal defects via subwavelength imaging. On the other hand, defect mode sensing may inspire the development of novel sensing systems for monitoring liquid properties. At the same time, the topological modes protected by duality symmetry may benefit unprecedented wave phenomena such as interference-free information transfer.