Moulding flexural waves in elastic plates lying atop a Faqir's bed of nails

摘要

Platonic crystals (PCs) are the elastic plate analogue of the photoniccrystals widely used in optics, and are thin structured elastic plates alongwhich flexural waves cannot propagate within certain stop band frequencyintervals. The practical importance of PCs is twofold: these can be used eitherin the design of microstructured acoustic metamaterials or as an approximatemodel for surface elastic waves propagating in meter scale seismicmetamaterials. Here, we make use of the band spectrum of PCs created with verysmall clamped holes, the nails of the title, to achieve surface wave reflectorsat very large wavelengths, a flat lens, an endoscope, a directive antenna nearstop band frequencies and cloaking from Dirac cones. The point pinned, Faqir,plate is particularly appealing as there is an exact dispersion relationavailable so the origin of these phenomena can be explained and interpretedusing Fourier series and high frequency homogenization.