EIGEN-OSCILLATIONS OF A TRANSVERSELY ISOTROPIC ELASTIC LAYER ATTACHED TO AN ISOTROPIC HALF-SPACE

Abstract

Layered media have waveguide properties - waves can propagate without sources in such structures. For the most part, such media are anisotropic ones. The simplest case of anisotropy is a transversely isotropic medium. The properties of such media are characterized by the fact that its elastic modules are the same in a plane perpendicular to the axis of symmetry, but they are different from the modules in the direction of the axis. As studies show, many sedimentary rocks are transversely isotropic. Besides, such structures are used in the production of composites. For example, if fibers parallel to each other are used as a reinforcing material, then the composite has a unidirectional structure and is transversely isotropic material in the planes perpendicular to the direction of reinforcement. Sheet metals are often non-isotropic ones, and have normal (transversal) anisotropy. Reinforced concrete is also considered as transversely isotropic after the appearance of cracks. Similar structures appear during the production of glued wood. Waveguide structures formed by a transversely isotropic layer conjugated to an isotropic half-plane are considered. Two waveguides are studied: one with a fixed wall, the other one with a free surface. The characteristic equations are constructed for them. The discrete and continuous spectra of these waveguide structures are singled out.