Volume 105, Number 5, March 2014
|Number of page(s)||6|
|Section||Electromagnetism, Optics, Acoustics, Heat Transfer, Classical Mechanics, and Fluid Dynamics|
|Published online||19 March 2014|
Moulding and shielding flexural waves in elastic plates
1 Department of Mathematics, Imperial College London - London, SW7 2AZ, UK
2 80 Capital LLP - London, W1S 4JJ, UK
3 Aix-Marseille Université, CNRS, Centrale Marseille, Institut Fresnel - 13013 Marseille, France
Received: 17 December 2013
Accepted: 23 February 2014
Platonic crystals (PlCs) are the elastic plate analogue of the photonic crystals widely used in optics, and are thin structured elastic plates along which flexural waves cannot propagate within certain stop band frequency intervals. The practical importance of PlCs is twofold: These can be used either in the design of microstructured acoustic metamaterials or as an approximate model for surface elastic waves propagating in meter scale seismic metamaterials. Here, we make use of the band spectrum of PlCs created by an array of either very small or densely packed clamped circles to achieve surface wave reflectors at very large wavelengths, a flat lens, a waveguide effect, a directive antenna near the stop band frequencies. The limit in which the circles reduce to points is particularly appealing as there is an exact dispersion relation available so the origin of these phenomena can be explained and interpreted using Fourier series and high-frequency homogenization (HFH). We then enlarge the radius of clamped circles, which both makes the zero-frequency stop band up to five times wider and flattens the dispersion curves. Here, HFH notably captures the essence of localized modes, one of which appears in the zero-frequency stop band and is used in the design of a highly directive waveguide.
PACS: 42.70.Qs – Photonic bandgap materials / 42.25.Bs – Wave propagation, transmission and absorption / 46.70.-p – Application of continuum mechanics to structures
© EPLA, 2014
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