Mechanical metamaterials for wave control: Effects of modularity and nonlinearity

Periodic structures have been a focus of research for decades due to their unprecedented wave-control functionalities. This has made them potential candidates for applications such as wave-filtering, vibration/seismic isolation, and wave-guiding. Periodic systems fall under two broad categories: phononic structures and metamaterials, both of which have been extensively investigated. More recent efforts focus on how to make these systems even more versatile and adaptable. As such, the objective of this dissertation is two-fold: 1. to investigate a modular approach to the design of metamaterials in an attempt to broaden the design space and achieve new wave-control functionalities that go beyond that of the conventional designs proposed. 2. to exploit nonlinearities for realizing passive-adaptive wave-control. In the former, we primarily focus on a special category of modular systems in which elements are entangled through periodic connections along their length. We explore the second area in the context of surface waves pursuant to our interest in potential seismic applications. We start by a theoretical investigation of dispersion properties for a metamaterial beam that consists of flexural elements periodically coupled (entangled) along their length. We will show that the structure possesses multiple Bragg scattering and local resonance band gaps, and has unique wave-filtering properties unlike its constituents. We will also show how static tuning of connection properties can be used to alter the system's band structure. Next, entangled monoatomic chains are considered in two configurations. One is a configuration where each mass in one chain is connected to its corresponding mass in the other chain (full coupling). The other, consists of chains that are periodically coupled only at certain locations (partial coupling). We derive closed-form dispersion relations for both cases and discuss their eccentric dynamic properties, such as double-speed wave propagation zones, emergence of negative group velocity dispersion branches and flat bands. For each study, we use numerical simulations to verify our theoretical results, and present example devices targeted at wave propagation control using finite prototypes of each meta-structure. In the remainder of this work, we focus our attention on embedding nonlinearity in the design of metamaterials to control surface waves in a passive-adaptive manner. First, we present an approximate theoretical framework for how Rayleigh waves interact with a periodic array of Duffing oscillators. Our analysis indicates that the presence of nonlinearities makes dispersion amplitude-dependent. We further show that for hardening (softening) nonlinearities, dispersion branches shift towards higher (lower) frequencies as the amplitude of motion increases. In the light of this promising preliminary results, we attempt to realize the phenomenon in an experiment. In order to do this, we leverage a compact experimental setup consisting of a plate, serving as an elastic substrate, and bead-magnet assemblies, in lieu of nonlinear resonators. We will study the dynamics of the constituting elements of this structure in detail to present, for the first time, experimental evidence of amplitude-dependent dispersion for surface acoustic waves. The findings of this two-part study will inform the design of more versatile metamaterials at different scales. Finally, we will also discuss some promising future directions that may be considered as both short-term and long-term extensions to this work.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Civil Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Hajarolasvadi, Setare

Contributors dc:contributor

• Elbanna, Ahmed E
• Fahnestock, Larry A
• Matlack, Kathryn H
• Vakakis, Alexander F

• phononics
• metamaterials
• modularity
• nonlinearity
• bandgaps
• wave-control
• amplitude-dependence
• dispersion
• tunability

Statement dc:rights

• Copyright 2021 Setare Hajarolasvadi

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/113318

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F113318