On the theory of smooth topographic waveguides for Rayleigh waves

In the present paper, it is demonstrated that the existence of guided modes of Rayleigh waves on some types of smooth solid surfaces, often called 'smooth topographic waveguides', can take place under the condition of total internal reflection of Rayleigh waves from the 'external' areas of surfaces surrounding the 'internal' areas of wave localisation. In the framework of the geometrical acoustics approximation, the possibility of total internal reflection of Rayleigh waves in smooth topographic structures of complex geometry is linked to the presence of internal areas on the surfaces characterised by the geometry-modified angular-dependent local phase velocities of Rayleigh waves that are smaller in the direction of guided wave propagation than their velocities in the surrounding external areas. The above-mentioned condition of wave localisation is illustrated by theoretical calculations of the dispersion curves of guided waves for several examples of guided wave propagation. The obtained results for the dispersion curves of localised waves are compared with the known solutions, where available.