An asymptotic model for the Stoneley interfacial waves.

This M.Sc. thesis is focused on studying interfacial waves for an asymptotic model evaluating the contribution of the Stoneley wave to the overall dynamic field.These interfacial waves are excited by loads or discontinuities on the interface. The work deals with the explicit model for Stoneley wave which are based on slow time perturbation. The model is developed in homogeneous, isotropic, elastic media. Stoneley wave is a generalised Rayleigh wave. For the Rayleigh wave, the explicit model was constructed by Kaplunov et al. in 2006. The asymptotic model has been useful to deal with various surface dynamics problems. Therefore we aim to construct an asymptotic model for Stoneley interfacial wave. In essence the model describes propagation of the wave by hyperbolic equation on the interface. The decay over the interior is governed by elliptic equations. We investigated interfacial problems with different boundary conditions, including the discontinuity in stresses or displacements. The proposed model consist of hyperbolic equation on the interface and elliptic equations on the inside. An illustrative example is presented for the case of normal loading with the solution obtained through the Poisson's integral formula.