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...[ Read more ]

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.