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The counterintuitive properties of photonic crystals, such as all-angle negative refraction (AANR) [J. Mod. Opt.34, 1589 (1987)] and high-directivity via ultrarefraction [Phys. Rev. Lett.89, 213902 (2002)], as well as localized defect modes, are known to be associated with anomalous dispersion near the edge of stop bands. We explore the implications of an(More)
The recently discovered undamped localized mode at the end of an elastic strip is demonstrated to be particularly relevant in the plane stress setting, where it exists for the Poisson ratio 0.29. This paper also emphasizes the difference between low-frequency edge modes, typically characterized by low variation across the plate (or shell) thickness, and(More)
The 2D equations in the Kirchhoff-Love theory are subjected to asymptotic analysis in the case of free interfacial vibrations of a longitudinally inhomogeneous infinite cylindrical shell. Three types of interfacial vibrations, associated with bending, super low-frequency semi-membrane, and extensional motions, are investigated. It is remarkable that for(More)
The paper describes the propagation of three-dimensional symmetric waves lo-calised near the traction free edge of a semi-infinite elastic plate with either traction free or fixed faces. For both types of boundary conditions, we present a variational proof of the existence of the low order edge waves. In addition, for a plate with traction free faces and(More)
This Letter deals with an analysis of bending edge waves propagating along the free edge of a Kirchhoff plate supported by a Winkler foundation. The presence of a foundation leads to a non-zero cut-off frequency for this wave, along with a local minimum of the associated phase velocity. This minimum phase velocity corresponds to a critical speed of an edge(More)
The dynamic response of a homogeneous half-space, with a traction-free surface, is considered within the framework of non-local elasticity. The focus is on the dominant effect of the boundary layer on overall behaviour. A typical wavelength is assumed to considerably exceed the associated internal lengthscale. The leading-order long-wave approximation is(More)
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