Wave Diffraction in an Elastic Medium with a Spherical Cavity Supported by a Thin Shell

The purpose of this work is to study the propagation and diffraction of unsteady waves on a thin spherical shell located in an elastic half-space. Analytical methods are used to construct the solution. The problems of diffraction of elastic waves on various types of inhomogeneities are among the most complex and topical problems of the dynamics of deformable bodies. From the applied point of view, this is explained by the fact that the information about the dynamic stress-strain state in the vicinity of these inhomogeneities is of great interest for various purposes. Moreover, the presence of inhomogeneities (inclusions, cavities, notches, local changes in properties, etc.) is an indispensable condition arising in various fields of modern engineering. Such tasks include: creation of new structures working under dynamic loads, development of new composite materials and their introduction in creation of engineering structures, modern tasks of geophysics and seismology, as well as a number of other tasks of scientific and technical character.