On the study of some geological structure models

Kuban State University, 149, Stavropolskaya str., Krasnodar, 350040, Russia

^* Corresponding author: pavlova@math.kubsu.ru

Abstract

In this work, we study problems of harmonic vibrations of extended elastic structures with a coating. The studied boundary value problems can have different physical interpretations; in this case, they are considered as models of geological structures. We used two different coating models. The equation of a bending plate was chosen to describe one of them. The second type of coating is not a traditionally studied stringer or overlay, since it is characterized by several parameters of a two-dimensional deformable object. Further we have conducted a study of the properties for the substrate/coating system. Where numerical analysis showed us that the difference between the zero and pole curves for an elastic medium with a coating from the dispersion curves for an elastic medium without a coating is stronger the greater the thickness of the coating plate and the denser its material. The conclusions are valid for both plate models used. The models of lithospheric structures considered in this work make it possible to study the features of wave propagation in a three-dimensional deformable foundation with a two-dimensional coating, not only for continuous coatings, but also in the presence of vertical defects in them, as well as heterogeneous composite coatings. The presented approach can be extended to problems for heterogeneous substrates.