Exact solutions for elastic surface waves with general lateral dependencies in layered structure

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Within this proposal we are planning to develop a theory for surface waves, with general lateral dependency. To gain some insight into the problem, this will initially be carried out in respect of structures composed of linear isotropic elastic layers. After these results have been established, a similar approach will be applied to investigate the influence of anisotropy and/or pre-stress. In respect of the isotropic case we expect to find a wide class of exact solutions, depending on depth and on the both lateral variables. These solutions will clearly show distinctly different behavior in both lateral variables. Among particular cases of interest, we expect to describe waves with plane wave fronts and polynomial transverse dependency. Various analytical methods will be employed for the appropriate type of partial differential equations associated with elastic continua which were mentioned in the Introduction. Both for comparison of analytical solutions and as an initial guide to aid analysis, we will rely heavily on advanced various asymptotic procedures used for wave propagation, especially in inhomogeneous media. This will include, for example, the ray method. The ray method is a method in which the proposed visiting Professor has significant international expertise. The layered structures may well require use of propagator and transfer matrix methods and the Stroh formulism, within both an anisotropic and/or pre-stressed theoretical framework.