THESIS
2019
xi, 81 pages : illustrations ; 30 cm
Abstract
Artificially structured materials, known as metamaterials, have been widely explored
for manipulating waves thanks to their unconventional properties beyond those found in
natural materials. Unlike natural materials whose properties are determined by their
chemical constituents, the physical properties of metamaterials depend largely on the
internal structures of their building blocks, and thus by designing the internal structures,
various properties/functionalities can be achieved. In the past two decades, many designs
have been proposed, resulting in a range of materials with a variety of exotic properties,
for example, negative refraction, super-resolution imaging, etc. However for practical
applications, in addition to the desired properties, various design requirements and...[
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Artificially structured materials, known as metamaterials, have been widely explored
for manipulating waves thanks to their unconventional properties beyond those found in
natural materials. Unlike natural materials whose properties are determined by their
chemical constituents, the physical properties of metamaterials depend largely on the
internal structures of their building blocks, and thus by designing the internal structures,
various properties/functionalities can be achieved. In the past two decades, many designs
have been proposed, resulting in a range of materials with a variety of exotic properties,
for example, negative refraction, super-resolution imaging, etc. However for practical
applications, in addition to the desired properties, various design requirements and
constraints such as broadband performance, robustness, multiple functionalities and
tunability are needed. The conventional physical-guided design approach often leads to
suboptimal solutions for design problems with multiple requirements. This thesis work
aims to develop inverse design approaches based on topology optimization for systematic
design of elastic metamaterials with multiple design objectives. A set of novel elastic
metamaterials/metasurfaces with robust performance and multi-functionalities has been
designed and verified numerically and/or experimentally.
Firstly, a two-step topology optimization scheme is proposed for dispersion
engineering of hyperbolic elastic metamaterials over a broad frequency range. The scheme
is formulated based on the physical nature of the hyperbolic dispersion and is solved by a
typical gradient optimizer. By manipulating the dispersion band structure, non-resonant
hyperbolic metamaterials have been successfully designed. Novel features/applications
such as negative refraction, wave partial focusing and super-resolution imaging have been
numerically demonstrated. The optimized designs outperform the traditional designs in
terms of working frequency bandwidth. Furthermore, polarization-dependent transmission
has been found in the designed metamaterial, which is a unique feature due to the
optimization scheme developed. The proposed two-step scheme is also applicable for
general dispersion engineering of metamaterials.
Secondly, a general design framework based on topology optimization is proposed for
the design of elastic metasurfaces with multiple requirements/functionalities. The proposed
design framework has been applied to design elastic metasurfaces with high-energy
transmission and robust performance. Multifunctional metasurfaces that can
simultaneously control longitudinal and shear wave have been designed and realized for
the first time. Furthermore, multi-frequency metasurfaces that can realize different wave
manipulation at different wave frequencies have also been designed. Such metasurfaces
can serve as tunable materials that can switch wave control mode simply by changing
operation frequencies. Compared with the existing tunable metamaterials, our
metasurfaces are passive and do not need any control/actuation schemes, and thus are much
easy to implement. Another application of the designed multi-frequency metasurfaces is to
use them as demultiplexers, which is useful in a range of practical applications such as
structural health monitoring and vibration control.
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