Abstract
Metamaterials are not deemed to be newly invented materials. They are artificially designed structures to unprecedentedly manipulate wave propagation. By arranging engineering microstructures at a sub-wavelength or even deep sub-wavelength scale into structures, various novel properties can be obtained, which do not exist in nature, such as the negative mass density, acoustic cloaking, etc. In general, two main mechanisms account for the occurrence of bandgap, i.e., Bragg scattering mechanism and local resonance mechanism. In a Bragg scattering type metamaterial, bandgap prohibits a wave from propagating through the structure with the wavelength of the same order as the lattice constant. For a low frequency bandgap, the system is constantly kept at a large scale. On the contrary, for a local resonance type metamaterial, the wavelength can be multiple orders greater than the dimension of locally resonant constituent units.Generally, bandgap ranges in a system can be obtained via two approaches. One is the exhibition of band structure or dispersion relation, i.e., the relation between frequency and wavenumber. Bandgap is a frequency regime where no band exists in the band structure. Another one is the discovery of transmission properties. Transmissibility is defined as a ratio of signals at the receivers and excitation points. However, band properties of a linear system attract more attention due to their efficiency in explaining most physical models. For some other soft materials, nonlinearity plays a significant role with large structural deformations. Thus, the bandgap properties of nonlinear systems are studied to understand more complex dispersion relations. Moreover, nonlinearity can be utilized to actively control the whole system and optimize the precision of the devices.
Based on the analysis of band properties, several topological points occur, such as the band crossing (BC) point, the Dirac cone (DC) and the double Dirac cone (DDC). Topology was initially a mathematical concept, which was further extended to the areas of physics, such as condensed matter physics and field theory in quantum mechanics. It can even describe the overall universal shape. To be specific, by disturbing the spatial symmetry in acoustic/elastic metamaterials, the BC point, DC and DDC can be easily broken, leading to the exhibition of topologically protected phase transition. Several topological invariants explicate for the phase transition, i.e., the Zak phase in a one-dimensional (1D) system and the spin/valley Chern number for two-dimensional (2D) Chern insulators. The topologically protected wave propagation can exhibit enormous distinctive properties, such as robustness and defect-immunity. Various waveguide path designs and reconfigurable wave channel switchers can be realized based on these properties.
Nevertheless, most of the previous studies focused on the passive response of wave propagation in metamaterials. Therefore, the working frequencies of the structure are fixed and within limited ranges. When it comes to a real-life application, it is difficult to change the working frequencies of these metamaterials upon the completion of the manufacturing process. Thus, active controls demonstrate outstanding potential and notable advantages in broadening the width and range of bandgaps. Typically, applied mechanical loads, temperature, magnetic fields, electric fields, nonlinearity and large deformations are critical choices for controlling the bandgap and topological properties of active metamaterials. These several active control approaches produce numerous benchmark results for new and practical metamaterial applications and designs.
Problems addressed in this thesis include but are not limited to linear dynamics, nonlinear dynamics, classical vibration problems, bandgap, Dirac Cones, spin/valley Chern numbers, Zak phase, tunable frequency response of topologically protected interface mode (TPIM) and waveguide design. Artificial structures based on several classical mechanical models, such as beam-foundation system, plate, underwater system, lattice system and pre-stretched membrane are designed. Moreover, several unique structures with distinguished properties, such as negative mass density, are analyzed. Regarding the linear dynamics, the plane wave expansion method (PWE) method and the transfer matrix method (TMM) are developed. Besides, the Lindestedt-Poincaré (L-P) perturbation method is utilized to solve nonlinear dynamic problems. Several cases using commercial engineering software COMSOL Multiphysics are also shared. Conclusively, the models, analytical and numerical methods are shown to be applicable to various problems addressed in acoustic metamaterials (AMs).
| Date of Award | 28 Jul 2021 |
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| Original language | English |
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| Supervisor | C W LIM (Supervisor) |