Propagation of skew-symmetric nonstationary waves in an elastic spherical layer.

The problems of propagation and diffraction of non-stationary waves in elastic bodies are of great theoretical and practical importance in such areas of science and technology as aircraft construction, shipbuilding, seismic exploration of minerals, seismic resistance of structures, and many others. The paper considers the problem of propagation of skew-symmetric nonstationary waves in an elastic spherical layer. To solve the problem, the integral Laplace transform with respect to dimensionless time and the method of incomplete separation of variables were used. In the space of images, the problem is reduced to an infinite system of linear algebraic equations, the solution of which is sought in the form of an infinite series in exponents, which makes it possible to obtain a solution to an infinite system without using the reduction method. Formulas are obtained for the components of the displacement vector and the stress tensor. The transition to the originals is carried out using the theory of residues. Numerical experiments were carried out, the results of which are presented in the form of graphs. The obtained results of the work can be used in the field of geophysics, seismology and design organizations in the construction of structures, as well as in the design of underground reservoirs. [ABSTRACT FROM AUTHOR]