Saudi Cultural Missions Theses & Dissertations
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Item Restricted Interface Modes in Elastic Metamaterials: A Closer Look at Topological Properties, Boundary Condition Effects, and Real-Time Tunability(University at Buffalo, The State University of New York, 2025-05) Alotaibi, Maha; Nouh, MostafaThe study of mechanical metamaterials has gone far ahead by incorporating topological ideas from condensed matter physics. This work covers topological mechanical metamaterials, representing a novel class of materials exhibiting unique wave propagation properties protected by topological states. Inspired by quantum topological insulators, these states enable waves to travel robustly through materials despite structural defects and imperfections. Therefore, by applying the topological invariants such as Zak phase, Berry phase, and Chern number, the work thereafter tries to work out the possibility of invariant structure modification with waveguiding control. Therefore, this research targets time-reversal symmetric systems and expands previous works concerning topological mechanical metamaterials by concentrating on previously neglected aspects. The first objective is to investigate how breaking spatial inversion symmetry affects 1D diatomic lattices. Previous literature has focused on stiffness-modulated lattices. However, the paper deals with mass-modulated lattices of uniform stiffness and analyzes their topological properties using the governing equations, dispersion relations, and Zak phase calculations. The study finds that mass-modulated lattices do not have the topological protection observed in stiffness-modulated systems, while both break spatial inversion symmetry. The second objective examines the role of boundary conditions in finite 1D periodic lattices. Employing free-free and fixed-fixed boundary conditions, the existence and stability of the tests topological edge and interface mode in the present study. The findings will demonstrate that the states of the topologically protected edges can only occur under some conditions where free boundaries exclude localization. In contrast, fixed boundaries ensure robust states at the edge. The present study further investigates the interface modes that can be formed when coupling two lattices with distinct topological properties, confirming that the so-called non-trivial interface modes remain stable for any variation of parameters. In contrast, trivial modes depend strongly on system configurations. The third aim is tuning the localized interface mode frequency within the bandgap by introducing ground springs, allowing precise frequency tuning without deteriorating the lattice. Numerical results confirm that the change of ground spring stiffness shifts the frequencies of interface modes proportionally and does not affect the system's topology. In this case, for two-dimensional (2D) hexagonal lattices, this study investigates the emergence of edge and interface modes at symmetric and asymmetric interfaces. While previous studies explored symmetric interfaces with identical bulk band structures, this work extends the analysis to asymmetric interfaces where bulk band structures differ. Dispersion analysis and transient simulations demonstrate that asymmetric interfaces can still support interface modes, although their robustness depends on the contrast in unit cell parameters. Additionally, the study evaluates how structural imperfections, such as sharp corners and disorders, influence interface modes, finding that topological waveguiding remains largely robust under these perturbations. A new contribution to this work is the proposition of a real-time waveguiding reconfiguration mechanism. In this case, changing dynamic unit cell parameters, this approach permits a smooth transition between different waveguide paths without any modification in the physical structure. The simulations demonstrate that wave propagation can remain confined along the designed paths, even with sharp bends and geometrical constraints. This opens new avenues for reconfigurable waveguiding and signal routing in practical applications. Finally, the results presented in this dissertation add to the general understanding of topological mechanics and its applications to multiscale structures. It will systematically investigate the interaction among spatial inversion symmetry, boundary conditions, and the stability of interface modes and thus provide insight into the design of tunable topological mechanical systems. In the future, these ideas can be extended to higher-dimensional systems, experimental validation, and engineering applications, including but not limited to vibration isolations, energy harvestings, and adaptive materials. This work generally represents an advance in mechanical metamaterials and introduces new strategies toward robust and tunable wave transports.18 0