Wave Propagation in Periodic Acoustic Metamaterials: from 1D to 3D

Citation

Kim, Gunho (2023) Wave Propagation in Periodic Acoustic Metamaterials: from 1D to 3D. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/dyq0-vm69. https://resolver.caltech.edu/CaltechTHESIS:03022023-175118888

Abstract

Wave propagation in periodic structures has been studied for centuries; for example, Newton derived the velocity of sound based on a linear lattice. Recently, advanced manufacturing techniques have led to the fabrication of geometrically complex architected materials with acoustic properties unattainable by their constituent materials. Such rationally designed structures are often called acoustic metamaterials and they can be engineered to transmit, block, amplify, or redirect acoustic waves. Subwave-length building blocks, typically periodic (but not necessarily so), can be assembled into effectively continuous materials to manipulate dispersive properties of vibrational waves in ways that differ substantially in conventional media. This thesis investigates rationally designed acoustic metamaterials, ranging from 1D to 3D, and how acoustic wave propagation can be controlled by these artificially structured composite materials for ultrasound-related biomedical applications.

I first explore 1D wave propagation in acoustic metamaterials to study the basic mechanics and relevant analysis skills. Bio-inspired helical mechanical metamaterials are designed and their normal modes are investigated. I demonstrate the ability to vary the acoustic properties of the helical metamaterials by perturbing the geometrical structure and mass distribution. By locally adding eccentric and denser elements in the unit cells, I change the moment of inertia of the system and introduce centro-asymmetry. This allows me to control the degree of mode coupling and the width of subwavelength band gaps in the dispersion relation, which are the product of enhanced local resonance hybridization.

Then I study 2D wave propagation in microlattice acoustic metamaterials for ultra- sound manipulation. When coupled with pressure waves in the surrounding fluid, the dynamic behavior of microlattices in the long wavelength limit can be explained in the context of Biot’s theory of poroelasticity. I exploit elastoacoustic wave propagation within 3D-printed polymeric microlattices to design a gradient refractive index lens for underwater wave focusing. A modified Luneburg lens index profile adapted for ultrasonic wave lensing is demonstrated via the finite element method and underwater testing, showcasing a computationally efficient poroelasticity-based design approach that enables accelerated design of acoustic wave manipulation devices.

Lastly, I show that tailorable 3D wave propagation can be achieved based on the findings from the previous chapters. Functional ultrasound imaging enables sensitive, high-resolution imaging of neural activity in freely behaving animals and human patients. However, the skull acts as an aberrant and absorbing layer for sound waves, leading to most functional ultrasound experiments being conducted after skull removal. A microscale 2-photon polymerization technique is adopted to fabricate a conformal acoustic window with a high stiffness-to-density ratio and sonotransparency. Long-term biocompatibility and lasting signal sensitivity are demonstrated over a long period of time (> 4 months) by conducting ultrasound imaging in mouse models implanted with the metamaterial skull prosthesis.

Thesis Files