A study of wave propagation in time-varying and non-Hermitian elastic media
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[EMBARGOED UNTIL 12/01/2026] Elastic wave control in solids traditionally focuses on time-invariant and Hermitian media, where wave frequency, momentum, and dispersion are fixed by constant and symmetric material parameters. Emerging theoretical advances show that relaxing these constraints opens fundamentally richer regimes of wave physics. Space–time duality provides a unifying viewpoint: mapping spatial processes into the time domain enables temporal refraction, frequency shifting, and dynamical waveform manipulation, while mapping temporal evolution into effective spatial dimensions reveals synthetic topological phenomena and higher-dimensional band structure. In parallel, generalized constitutive and symmetry-breaking mechanisms further expand elastic dynamics. Non-Hermitian elasticity introduces asymmetric coupling, and Willis media add momentum–strain and stress–velocity interactions that generate intrinsic nonlocality and break reciprocity. Although each framework enriches wave behavior in distinct ways, their combined effects remain largely unexplored, and a unified understanding of how non-Hermitian and Willis mechanisms interact is still missing. These perspectives identify a broad frontier in which temporal modulation, synthetic dimensions, and generalized constitutive behavior collectively enrich the landscape of mechanical wave phenomena. Yet despite their promise, these concepts remain insufficiently unified and lack comprehensive experimental validation in elastic systems. First, this dissertation establishes the experimental foundations of space–time duality in elastic media by realizing temporal refraction and reflection of flexural waves in a time-modulated metabeam. Through sub-microsecond control of bending stiffness, sharp temporal interfaces implement the timedomain analogs of Snell's and Fresnel's laws, enabling direct observation of momentum conservation, frequency conversion, and waveform redistribution across temporal boundaries. Additional smoothly varying modulations achieve temporal impedance matching, waveform morphing, and programmable frequency shifts, demonstrating time modulation as a practical and powerful degree of freedom for elastic wave control. Second, the dissertation demonstrates topological pumping of Rayleigh surface waves by mapping temporal evolution onto a synthetic spatial dimension encoded by the phason degree of freedom in a quasiperiodically patterned metasurface. Adiabatic sweeping of the phason traces a closed loop on a synthetic torus and produces quantized edge-to-edge transport protected by a non-zero Chern number. This experiment provides a direct mechanical realization of higher-dimensional topological physics in a two-dimensional elastic platform, confirming that synthetic dimensions allow temporal concepts--such as quasienergy winding and adiabatic pumping--to emerge through purely spatial patterning. Third, a dynamic homogenization framework is developed for metabeams containing active or self-sensing scatterers, yielding a non-Hermitian Willis medium that captures frequency- and wavenumber-dependent inertia, stiffness, and cross-coupling. This effective model reproduces the full complex dispersion across the Brillouin zone and reveals a range of non-Hermitian and nonlocal behaviors, including directional amplification, shear-enhanced flexural modes, and non-Hermitian skin localization under open boundaries. By formulating a non-Bloch band theory and deriving a closedform bulk–boundary correspondence within the Willis continuum, the framework analytically connects spectral winding under periodic boundaries to spatial mode localization under open boundaries, establishing a general route to non-Hermitian topological mechanics. Together, these studies show that elastic structures provide a powerful and versatile platform for integrating time-varying modulation, synthetic-dimensional mappings, and non-Hermitian–Willis coupling within a unified physical framework. The insights developed in this dissertation broaden the conceptual and practical design space of mechanical metamaterials, demonstrating that temporal structure, synthetic dimensions, and generalized constitutive behavior form complementary degrees of freedom for shaping wave dynamics. This unified perspective points toward programmable and dynamically reconfigurable architectures that leverage time as a central design dimension, offering promising routes for future advances in mechanical wave control, topological transport, and active metamaterial technologies.
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Ph. D.