On the modeling of Slow Oscillations and Static Interaction of Lithospheric Units

The mechanical concept of assessing the seismicity of territories is based on the determination of stress concentration zones in lithospheric structures, which is one of the signs by which one can judge the places of possible seismic events. The study is aimed at the development of mechanical and mathematical models and methods for studying the stress-strain state of geophysical structures subject to static loads, as well as low-frequency harmonic loads. The paper presents a method for solving problems of the static interaction for a system of coating plates with an elastic substrate. In this model, the equations for displacements of the front surface and contact stresses are constructed on the basis of the solutions for the matrix-functional Wiener-Hopf equations, to which the original problem is reduced. A feature of the equations obtained is the presence on the right side of unknown functionals of the solution and its derivative, which are determined from a system of linear algebraic equations. Based on the developed approach, we presented a method for determining all the main characteristics of the stress-strain state of a block structure formed by two contacting plates on a deformable base. Along with the static problem arising in the study of factors affecting the geological structures strength properties, the paper also considers the problem for long-period steady oscillations of the coating/substrate system. For low frequencies, we propose to proceed to the sequential solution of several static problems.

coated medium, static load, harmonic source, straight line fault, eigen function method