Examination of Bi-Orthogonality Relationships in Elastic-Fluid Media

摘要

The bi-orthogonality relationships for vertically heterogeneous porous media in contact with various surfaces have been previously established. For the special case in which the porous substance has zero porosity, the relationships reduce to those for elastic media. The bi-orthogonality relationship for a fluid loaded elastic slab will be considered numerically by discretizing the boundary value problems using finite differences. The resulting matrix will be analyzed for the purpose of determining eigenvalues of the complex dispersion relationship of the layered media, as well as discerning the corresponding eigenvectors which are discrete analogies of the propagation/ evanescent eigenfunctions of the media.