Propagation of skew-symmetric unsteady shear waves from thick-walled shell in elastic space

Karshi State University, Karshi, 180103, Uzbekistan

^* Corresponding author: shukurovamon@yandex.ru

Abstract

Problems of propagation and diffraction of nonstationary waves in elastic bodies are of great theoretical and practical importance in such fields 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 the propagation of skew-symmetric unsteady shear waves from a thick-walled spherical shell in elastic space. To solve the problem, the integral Laplace transforms in dimensionless time, and the method of incomplete separation of variables was used. In the image space, the problem is reduced to an infinite system of linear algebraic equations, the solution of which is sought in the form of an infinite exponential series. Formulas for the displacement vector components and the stress tensor are obtained. The transition to the originals is carried out using the theory of residues. Numerical experiments have been carried out, the results of which are presented in graphs. The obtained results of the work can be used in geophysics, seismology, and design organizations in the construction of structures and in the design of underground reservoirs.