О резонансах академика И.И. Воровича в контактных задачах с деформируемым штампом в сейсмологии

Abstract

In this paper, for the first time, methods for obtaining resonant frequencies in plane and spatial contact prob-lems for deformable stamps are presented in a complex. Their existence was predicted by academician I.I. Vorovich. He constructed one-dimensional models of de-formable stamps consisting of a rigid stamp and a spring, illustrating the occurrence of resonances. Currently, thanks to the use of block element methods, it has become possible to investigate real contact problems with a deformable stamp. Earlier in the works of the authors, the existence of a new type of earthquakes, called starting, was established. In the course of the study, some functionals remained uncomputed, the role of which was not clear. It is shown that they serve to construct dispersion curves giving resonant frequencies predicted by academician I.I. Vorovich. A study is carried out for different types of contact problems and shows how the method of constructing dispersion equations becomes more complicated, both due to the complication of the shape of stamps and the complication of the rheologies of deformable stamps. Semi-infinite and deformable stamps of simple rheology in the form of a quarter plane are considered. In addition, a semi-infinite stamp with the rheology of Kirchhoff plates is analyzed. The obtained results provide an answer to one of the methods of constructing dispersion equations for I.I.Vorovich resonances in contact problems for different deformable stamps. The study is closely related to the identification of new precursors of seismicity, as well as to solve some problems in the theory of strength.