Abstract
Recently, metamaterials have been extended toward elastic waves in solids from previously prevailing investigations in classical waves. Complicated degrees of freedom of the constitutive relation for elastic waves have hindered progress in the research field but have also resulted in surprisingly rich physics. This provides a valuable platform for exploring the potential applications of metamaterials, including negative refraction, noise reduction and invisible cloaking. In this thesis, I will purposely exploit the complexity and opportunities that can be offered by elastic metamaterials.
A rapid progress of wave manipulation has been achieved due to the development of transformation optics (TO), based on the form-variance of Maxwell equations. However, for some TO devices with extreme function, it’s difficult to realize the singularity with extreme index. Based on the extension of classical plate theory, I implement a series of singular Eaton lenses with different refraction angles in the elastic curved plate. This feasible elastic framework can serve as a general methodology for manipulating wave propagation by relating the 2D index profile to the 3D thickness profile. By approaching zero thickness in the curved plate, the refractive index also approaches infinity, opening up new opportunities to explore unprecedented phenomena, such as the "blackhole" effect, which enhances the absorption of flexural waves near singularities.
Different from EM wave, the classical elastic wave equations are not invariant after the coordinate transformations, encouraging us to explore more sophisticated material properties. Willis coupling is an analogous concept to bianisotropy in electromagnetism, the additional coupling terms which relate stress to velocity (momentum to strain) keep the form-invariance under transformations, and it has already been observed in flexural modes utilizing bending local resonance. In this study, I investigate Willis coupling in torsional waves and experimentally verify asymmetric reflection and additional Willis coupling terms in the constitutive relationships. Furthermore, I extend this concept to the combination of flexural and torsional waves using effective medium theory in the subwavelength limit, and the mode conversion between these two types of waves leads to asymmetric reflection and transmission.
The counterintuitive constitutive relationships may enable us to manipulate the dispersion of elastic waves by inducing local resonance. Moreover, recent research has shown that nonlocality with long-range interaction can achieve non-trivial modes at low frequencies and has potential for tuning dispersion. By designing an “overpass” structure with two orthogonal “bridges”, I numerically and experimentally verify the birefringence of the single polarization for flexural waves related to the unusual “double flexural” modes in the subwavelength region.
For all these examples of elastic metamaterials from simple to complex constitutive relationship, I have used both full-wave simulations and field-mapping experiments to verify the associated band structures, constitutive parameters. Then, I tend to help experimentally realize some other unique concepts in elastic metamaterials, such as topological corners in arbitrary polygonal domains by applying aperiodic modulations. which may be applied to many mechanical devices in the future.