Tailoring elastic wave propagation at the macro and microscale via intentional nonlinearity

Elastic waves are fundamental to many natural and engineering systems. They sustain our auditory sense and speech mechanism. They also offer non-intrusive imaging techniques in medicine, oceanography, and autonomous vehicles. At the micro and nanoscale, they transmit signals in smartphone components, and, when operating at high frequency, elastic waves interact with electrostatic, electromagnetic and thermal/phononic signals. These controlled interactions enable new opportunities for device concepts and signal manipulation owing to the strong nonlinearities accessible to elastic waves. There is a need to fully exploit the potential of elastic waves by controlling and manipulating their propagation. Accordingly, this dissertation aims to tailor linear and nonlinear elastic waves through nonlinear structures and acoustic metamaterials. In general, nonlinear dynamics allow for behaviors that are not accessible in linear regimes, such as amplitude- frequency tunability, modal coupling, and internal resonances. Nonlinear metamaterials can alter the reciprocity that governs all linear time-invariant (LTI) systems, despite inhomogeneities and damping. Reciprocity leads to action-reaction responses that are interchangeable between any two points in a system, preventing diode and logic operations of elastic waves. In this dissertation, we implemented elastic wave redirection and nonreciprocity at the macroscale in two weakly-coupled-nonlinear waveguides via Landau-Zener tunneling (Chapter 2). This study experimentally showed different responses depending on the energy input: wave localization for low-energy inputs and nonreciprocal wave redirection for high-energy inputs. Switching to the microscale, we observed that buckling of micro-fabricated waveguides eliminates the transmission within the fundamental (i.e., lowest frequency) passband (range of frequencies where elastic waves are permitted to propagate), corresponding to a phase change in the metamaterial sense (Chapter 3). This phase change originates from the fabrication impurities that magnify with buckling, leading to an effective aperiodicity analogous to Anderson localization in electromagnetics. Encouraged by this effect of buckling, we examined the thermal and electrostatic control of buckling in micro-resonators (Chapter 4). Experimentally, we found that electro-thermoelastic buckling tunes the natural frequency of the resonators from 4.7 to 11.3 MHz, a factor of 2.4× tunability. In addition, the imposed buckling switches the nonlinearity of the resonators between purely stiffening, purely softening, and even softening-to-stiffening. To explain this buckling ultra- tunability, we developed a lumped reduced-order model (ROM) that replicated the linear (within 5.5% error) and nonlinear tunability (with errors depending on the electro-thermal conditions). Aiming to benefit from the buckling ultra-tunability, we computationally designed waveguides controlled by electro-thermoelastic buckling (Chapter5). We analyzed their transmission under different buckling conditions and experimental impurities, where Anderson localization reappeared. We also designed the waveguide with elastic nonreciprocity, which we will try to optimize in future work. In conclusion, the electro-thermoelastic buckling enabled powerful nonlinear elastic properties for wave tailoring. We presented the design and implementation methods that will hopefully assist future developments.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mechanical Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2023

Author dc:creator

• Kanj, Ali

Contributors dc:contributor

• Tawfick, Sameh
• Vakakis, Alexander F
• van der Zande, Arend
• Fang, Kejie

• Elastic Waves
• Nonlinearity
• Nonreciprocity
• Buckling
• Mems

Statement dc:rights

• Copyright 2023 Ali Kanj

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/120487

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F120487