Exploring Advanced Topological Metamaterials for Elastic Wave Manipulation
Creators: name: Dorin, Patrick
Publisher: name: My University
Year: 2023
Subjects: subject: mechanical metamaterials
subject: topological metamaterials
subject: elastic wave propagation
subject: waveguide
subject: topological phases of matter
subject: vibration control
subject: Mechanical Engineering
subject: FOS: Mechanical engineering
subject: Engineering

description: Elastic metamaterials enable control over the propagation of vibrations and elastic waves in mechanical structures, a useful feature that has been employed in numerous applications, such as energy harvesting, seismic mitigation, vibration and noise mitigation, sensing and imaging, and information processing. Recently, researchers have incorporated topological phase theory from condensed matter physics into elastic metamaterials to attain new functionality and robustness. Elastic wave control with these so-called topological metamaterials is immune to unwanted performance degradation in the presence of structural imperfections. Topological metamaterials also facilitate the manipulation of elastic wave energy in nearly arbitrary directions and serve as excellent macroscale platforms to investigate quantum transport physics. While topological metamaterials have demonstrated extraordinary control over elastic wave propagation, research gaps exist that are hindering their implementation in technical applications and provide opportunities for advancement. Easily integrated (i.e., compact) topological metamaterials that provide comprehensively adaptable wave control have yet to be developed. Furthermore, the topological metamaterials studied to date are often constrained to function over a fixed, singular, and narrow frequency bandwidth. Finally, despite plenty of studies on 1D and 2D topological metamaterials, topological phases in 3D and fractal mechanical systems have yet to be fully explored. To address the research gaps and advance the state of the art, this thesis explores a new class of advanced topological metamaterials that achieve responsive, broadband, easily integrated, and multidimensional elastic wave control and uncover new knowledge in topological and elastic wave physics. To achieve the research vision, the suite of novel topological metamaterials presented in this dissertation is synthesized through the understanding and harnessing of comprehensive on-demand adaptivity, local resonance, higher-order topological phases, and the rich dimensionality of 3D mechanical structures. Four novel topological metamaterials are created and investigated in this dissertation. First, a 2D topological metamaterial is synthesized that harnesses resonant piezoelectric circuitry for comprehensively tunable elastic wave control. This innovative metamaterial unlocks the capability to concurrently adjust the path, shape, and frequency of topological states, operates over a broad and subwavelength frequency bandwidth, and facilitates a new understanding of adaptive topological wave control. Next, a 3D topological metamaterial is proposed that can be tuned on-line through metastable elements. By taking advantage of the adaptivity of this 3D metastable metamaterial, the path of 2D topological surface states is on-demand controlled for the first time, a bilayer-locked topological state is discovered, and 3D elastic wave networks with unprecedented dimension-switching, filtering, and splitting capabilities are realized. Taking inspiration from the first two studies, a novel 3D topological metamaterial is created that exploits multimodal local resonance to achieve wave control that is low-frequency, multiband, and polarization-dependent. Outcomes from this work include the first full-field experimental measurements of a 2D topological state and multi-polarized waveguides in a 3D mechanical structure. Finally, higher-order topological phases and multimodal resonance are used to synthesize a 2D topological metamaterial that attains 0D and 1D topological waveguides across multiple frequency bands. The unique capabilities of this novel metamaterial are employed to investigate topological wave control in fractal geometries and realize wave-based mechanical logic gates. Overall, this thesis presents groundbreaking results in elastic wave control, establishing unprecedented capabilities that hold promise for a diverse set of engineering applications. Moreover, this research uncovers new fundamental insights into the interplay between topological and elastic wave physics, with implications across multiple disciplines in the physical sciences.