Controlling Acoustic and Elastic Waves With Metamaterials: Design Elements and Their Application

The purpose of this dissertation is to model, simulate and design metamaterials for underwater sound and elastic wave control. Water-based acoustic metamaterials usually suffer from low transmission due to the impedance mismatch with water; elastic metamaterials also suffer from this issue not only because of the impedance mismatch to the host medium, but also due to the multiple wave types existing simultaneously at the interface between the inclusions and the background matrix. This dissertation focuses on the theoretical modeling and computational design of broadband high transmission metamaterial devices.;Several related topics are discussed. (1) A semi-analytical method for band diagram computation of three dimensional (3D) lattices is developed in this dissertation. It has significant applications in 3D pentamode metamaterial design. (2) Acoustic transmission through gratings of parallel plates displaying anisotropic inertia is also investigated. It is found that broadband impedance matching and total acoustic transmission can be achieved if the plane wave is incident at the so-called intromission angle +/-theta i. (3) Elastic wave transmission through aligned parallel plates are studied theoretically by considering the coupling between different types of waves in elastic half-spaces and in the plates. The results are applied in the design and optimization of elastic metamaterials. (4) Elastic waves in fluid-saturated anisotropic double porosity medium of cubic symmetry is also investigated as an extension to Biot's theory of poroelasticity. A third dilatational wave is predicted in a double porosity fluid-saturated gyroid structure and demonstrated using finite element (FEM) simulations.;The second part of the dissertation focuses on several novel devices for manipulating acoustic and elastic waves. Metallic metamaterial unit cells of the hexagonal lattice type are employed to mimic the quasi-static acoustic properties of water, and to provide a certain range of index for gradient index (GRIN) metamaterial design. The advantage of such a metamaterial element is that it has in-plane isotropy and only allows one propagating mode within the frequency range of interest. (5) A flat GRIN lens is designed by tuning the unit cells to obey a modified hyperbolic secant index profile, such that a normally incident plane wave transmits through the lens efficiently and focuses at a single point. The side lobe suppression and aberration reduction abilities of the GRIN lens are demonstrated in both simulations and in underwater experiments (carried out by colleagues at the University of Texas at Austin). (6) An elastic shell based metamaterial element, which provides a wider range of index at the quasi-static regime, is adopted in the design of a conformal lens for converting a monopole source to highly directional plane wave beams. The required bulk modulus and density distributions are derived using conformal transformation acoustics mapping from a unit circle to a triangle. The mapping function is adjustable which allows energy radiating preferentially into different directions. Two collimation devices are designed using fluid-saturated shells and demonstrated using full wave FEM simulations. (7) A novel class of elastic metamaterial composed of "effective plates" are introduced to design high transmission devices for elastic waves. Several devices for focusing SV-wave, splitting P- and SV-waves, and asymmetric transmission are designed and demonstrated using full wave FEM simulations.