THESIS
2023
1 online resource (viii, 98 pages) : color illustrations
Abstract
Recently, metamaterials have been extended to elastic waves in solids, departing from
the previously prevailing investigations in electromagnetic and acoustic waves. The intricate
degrees of freedom in the constitutive relations for elastic waves have both hindered progress
in the research field while yielded surprisingly rich physics on the other hand. This provides a
valuable platform for exploring potential applications of metamaterials, including negative
refraction, noise reduction, and invisible cloaking. In this thesis, elastic metamaterials are
explored from conventional to complex constitutive relationships and unique dispersion.
Here, I focus on elastic waves propagating on plates and beams. First, a series of singular
Eaton lenses is implemented with different refraction angl...[
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Recently, metamaterials have been extended to elastic waves in solids, departing from
the previously prevailing investigations in electromagnetic and acoustic waves. The intricate
degrees of freedom in the constitutive relations for elastic waves have both hindered progress
in the research field while yielded surprisingly rich physics on the other hand. This provides a
valuable platform for exploring potential applications of metamaterials, including negative
refraction, noise reduction, and invisible cloaking. In this thesis, elastic metamaterials are
explored from conventional to complex constitutive relationships and unique dispersion.
Here, I focus on elastic waves propagating on plates and beams. First, a series of singular
Eaton lenses is implemented with different refraction angles on an elastic plate with spatially
varying thicknesses. This implementation framework serves as a general methodology for
manipulating flexural wave propagation by linking a two-dimensional refractive index profile
to its corresponding thickness profile of the plate and is particularly useful for designing
transformation-elastic devices driven by coordinate transformations. Very often, these devices
will generate singular refractive indices, which can now be realized by approaching to a small
thickness of the plate. While an Eaton lens with a singular index profile is an immediate application, I have also explored and experimentally demonstrated the analog black hole effect
based on conformal mapping by using a scalar wave approximation for the flexural wave
propagation on an elastic plate so that merely a refractive index profile description is adequate.
On the other hand, it is now well-known that the full set of elastic wave equations are not
form-invariant upon a general coordinate transformation. The incorporation of the Willis
coupling, an analog concept to bianisotropy in electromagnetism, is one way to restore the form-invariance.
The Willis coupling is actually a new constitutive parameter that relates stress to
velocity and momentum to strain in the level of constitutive relationship. While it has been
realized initially in air-borne acoustic waves and also elastic flexural waves on a beam, here
such concept has been extended to other kinds of mechanical waves, such as elastic torsional
waves, a combination of flexural and torsional waves, and surface water waves by incorporating
local resonating structures together with mirror symmetry breaking in the propagation direction.
A general numerical procedure, based on extracting the local field amplitudes with full-wave
simulations and multiple types of excitations, has been developed to extract the full constitutive
matrix of the metamaterial in one dimension. In these cases, the Willis coupling can be revealed
both theoretically and experimentally through asymmetric reflection and asymmetric mode
conversion due to different wave impedances in forward and backward propagating directions.
More recently, by exploiting non-locality and long-range interaction among structures
within a single unit cell, additional modes at low frequencies, i.e. birefringence or more than
one refractive index, become possible. By incorporating an “overpass” structure within a unit
cell of flexural-wave metamaterial, more than one flexural modes can be realized at an arbitrary
low frequency, termed as birefringence of single polarization. For all these examples of elastic
metamaterials, I have explored unconventional constitutive parameters, including large
refractive indices, analog of bianisotropy, asymmetric impedances and birefringence for the
same polarization at low frequencies, with potential applications in transformation-elastic
devices, asymmetric reflection and transmission, and topological band structures.
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