Author: An, Shuowei
Title: Manipulation of mechanical waves with meta-structures
Advisors: Zhu, Jie (ME)
Cheng, Li (ME)
Degree: Ph.D.
Year: 2023
Subject: Quantum theory
Hong Kong Polytechnic University -- Dissertations
Department: Department of Mechanical Engineering
Pages: xviii, 156 pages : color illustrations
Language: English
Abstract: Metamaterials refer to materials or structures artificially architectured to support intriguing effects that cannot exist in nature. In recent years, this ever-expanding field has been greatly inspired by newly emerging concepts in quantum mechanics, thus creating an unprecedented degree of freedom and design space for unconventional wave manipulation. This thesis introduces and explores three physical concepts, non-Hermiticity respecting parity-time (PT) symmetry, topology insulator, and bound states in the continuum, into mechanical wave systems to achieve several anomalous wave effects.
This thesis starts with a theoretical exploration of the unidirectional invisibility of PT-symmetric acoustic and elastic wave systems. An analysis of the acoustic wave interference within a PT-symmetric layered medium shows that, different from optical waves, the material parameter that governs the exceptional points of the scattering matrix is acoustic impedance instead of refraction index. Yet for elastic waves, the coupled-mode theory shows that wave speed is the crucial parameter affecting the flexural wave propagation in a beam. More general conditions of unidirectional invisibility are also derived by including unequal modulation amplitudes and rectangular wave modulation.
The next chapter focuses on manipulating the localized states in a topological phononic crystal plate, including edge and corner states. Discrete models are adopted as a versatile platform to show the salient topological effects, such as topological phase transitions. The edge states can be routed by introducing anisotropic couplings in a square lattice. It is shown that the topological phases along different directions can be independently controlled to support directional edge states. When the bands along the two directions are tuned to be topologically untrivial, coexisting edge states can possess distinctive frequency ranges, giving rise to the frequency-routed properties. Not limited to the edge states, the manipulation can also be extended to the corner states of the second-order topological insulator, which can be selectively turned on or off by engineering the valley positions. In particular, by strengthening the next nearest neighbor coupling, the polarization of the corner states can go beyond the symmetric to anti-symmetric ones.
Finally, localized modes are constructed through a distinctive mechanism: bound states in the continuum (BIC). The coupled-mode theory predicts that a symmetric pillared Lamb waveguide enables multi-polarization BICs, including both symmetric and antisymmetric branches. The near-field coupling between the separated pillars allows the existence of an unconventional Friedrich-Wintgen antisymmetric BIC, in which the resonators are not at the same site. More remarkably, the BICs of flexural wave with shorter wavelength than longitudinal case and the concentrated energy distribution in between the pillars, exhibit enhanced sensitivity to the in-between perturbation. The BICs of longitudinal wave, however, are almost immune to such perturbation. The two branches of BICs shift uniformly against the perturbation from the environment. Based on this, a BICs-assisted probe is proposed to detect potential structural defects. The technique offers increased sensitivity to structural damage and enhanced robustness to environmental fluctuation. Our study reveals rich properties of the BICs in elastic medium and holds great promise in developing functional sensing devices for other applications beyond structural health monitoring.
Rights: All rights reserved
Access: open access

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