Localised elastic waves in structures of complex geometry

In the present paper, it is demonstrated that the existence of localised elastic modes in structures of complex geometry can take place under the condition of total internal reflection of Rayleigh or plate waves from the areas surrounding the 'internal' areas of wave localisation. The possibility of total internal reflection in structures of complex geometry is often linked to the presence of internal areas on the surfaces characterised by lower values of the geometry-dependent local phase velocities of Rayleigh or plate waves in comparison with their values in the surrounding areas. The above-mentioned condition of wave localisation is illustrated by theoretical calculations of frequency-dependent phase velocities for three different cases of localised elastic wave propagation. These are localised Rayleigh waves propagating along solid cylinders of variable curvature, localised flexural waves in slender elastic wedges (also known as wedge elastic waves), and localised quasi-flexural waves in non-circular cylindrical shells.