Weak Spatial Dispersion of Elastic Waves in Anisotropic Solids

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This proposal seeks finance to bring over to the UK a leading international authority in waves propagation and physical acoustics for two visits totalling four months. In particular, we aim to investigate the propagation of waves in anisotropic elastic media which possess a micro-structure. The existence of a micro-structure, such as a fibrous inclusion, lead the wave speed being dependent on wave number, this usually being termed spatial dispersion. The specific type of waves to be considered are those for which the wavelength is long compared to a typical dimension of the particular micro-structure. For such waves, the spatial dispersion brought about by the micro-structure will smooth the singularities at the wave fronts associated with the associated non-dispersive media. Using various mathematical methods (singular perturbation, Fourier-type integrals and Catastrophe Theory) previous developed and exploited by the UK team, it is envisaged that the project will result in a complete classification