Date of Award

6-2-2018

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Systems Engineering

First Advisor

Eric Sandgren

Abstract

Metamaterial are materials engineered to have more than one property that cannot be observed in nature. Commonly, they are made from assemblies of multiple elements fashioned from composite materials such as metals or plastics. Due to its diverse application such as elastic wave cloaking, focusing and absorbing, elastic metamaterial has been the subject of intense experimental research and theoretical work in the past decades. Despite this large-scale effort, designs of the unit cell of the periodic structure for achieving negative elastic moduli are still needed. In this thesis, we first studied the wave phenomenon in lattice structure and materials with anisotropic negative material elastic properties. The study based on lattice structures revealed that the negative materials properties such as negative density and young’s modulus can be obtained through local mass-in-mass resonant. Multiple stop bands are also found in the band structure of the two-dimensional model. Anonymous wave propagation in homogeneous material with anisotropic negative material properties are studied theoretically. We then proposed two types of elastic metamaterials with its unit cell comprising locally chiral inclusion that can generate both translational resonance and rotational resonance. The first design is a single-phase elastic metamaterial with chiral microstructure that aims to obtain attenuation and negative reflection of elastic waves. To improve the performance of the elastic metamaterials, the second design is proposed by combining honeycomb lattice with chiral inclusions. Plane wave propagation in infinite periodic cells of those two elastic metamaterials is investigated through using Floquet-Bloch principles and finite element method. Stop bands, which are owing to different mechanisms, are found in the band structures of both of those two designs. Negative pass bands, which are a sign of negative refraction, appear in the band structures of wave propagation in those two metamaterials. The working mechanisms of those negative pass bands are revealed though analyzing the eigenmodes of the unit cell and the dynamic effective material properties. Numerical examples validate the proposed models and show that, attenuation and negative refraction of elastic waves in the elastic metamaterials have been obtained. The design concept of elastic metamaterials may be extended to the design of broadband flat lens for elastic wave focusing. In addition, based on the previous research result we already obtained, the work plan and implications are illustrated at the end of this proposal. The contribution of this work is providing the fundamental methodology for the design of elastic metamateials and could be useful for the application of wave guides and focusing lens.

Download

Share

COinS