Abstract
We consider the canonical problem of an array of rods, which act as resonators, placed on an elastic substrate; the substrate being either a thin elastic plate or an elastic half-space. In both cases the flexural plate, or Rayleigh surface, waves in the substrate interact with the resonators to create interesting effects such as effective band-gaps for surface waves or filters that transform surface waves into bulk waves; these effects have parallels in the field of optics where such sub-wavelength resonators create metamaterials in the bulk and metasurfaces at the free surfaces.Here we carefully analyse this canonical problem by extracting the dispersion relations analytically thereby examining the influence of both the flexural and compressional resonances on the propagating wave. For an array of resonators atop an elastic half-space we augment the analysis with numerical simulations. Amongst other effects, we demonstrate the striking effect of a dispersion curve which corresponds to a mode that transitions from Rayleigh wave-like to shear wave-like behaviour and the resultant change in the fields from surface to bulk waves.
Highlights
Metamaterials, as synthetic composite materials with a structure such that they exhibit properties not usually found in natural materials, form a major emerging research area that barely existed before 2000; the term “Metamaterial” itself was first used in 1999
The applicability of metamaterials to seismology has sparked the interest of geophysicists in the development of novel methods to control surface waves
Given the interest in this emerging area, there is a need to study the properties of the solutions to fundamental canonical problems
Summary
Metamaterials, as synthetic composite materials with a structure such that they exhibit properties not usually found in natural materials, form a major emerging research area that barely existed before 2000; the term “Metamaterial” itself was first used in 1999. This naturally leads in the full elastic situation of an array atop an elastic half-space, Section 3 investigates this and again explicit results emerge that are used to interpret and predict metamaterial/ metasurface phenomena.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
