Thin Layers in Elastic Wave Propagation -Effective Modelling and Diffraction

Doktorsavhandling, 1992

In the present thesis, the interest is focussed on the problem of effective modelling of thin interface layers for applications in elastic wave scattering. The layers are considered to be thin compared with wavelengths involved and it is shown that when all effects to lowest order in the layer thickness are included, we get boundary conditions (BCs) which have a number of nice features, including the one of implying that no scattering occurs when the layer has material parameters identical to the ones in the matrix medium. The layers are replaced by a single surface of discontinuity for the field variables, and the discontinuities are specified in such a manner that the influence of the original layer is reproduced locally to within O(h^2), where h is the layer thickness. Layers of fairly general shape, but of constant thickness, are considered. The BCs obatined are more complicated than the simple spring contact BCs, but they have the obvious advantage of containing all effects to the order indicated. The approach is possible to use in conjunction with almost any method for solving scattering problems. In this thesis the developed approximation thechnique is used in solving some potentially useful canonical scattering problems by the Wienr-Hopf method. The problems considered are scattering of time-harmonic horisontally polarized shear waves from swmi-infinite planar elastic (both isotropic and anisotropic) layers, and diffraction of L-TV waves from a fluid layer extending from an open crack imbedded in an elastic medium. The solutions can be used as building blocks in a more extensive investigation of finite layers, using the Geometrical Theory of Diffraction (GTD).