The three-dimensional problem of steady oscillations of an elastic half- space with a spherical cavity (Q579004)

The three-dimensional problem of the dynamic theory of elasticity concerning steady harmonic oscillations of an elastic half-space with a spherical cavity is considered. The problem is reduced, with help of the superposition principle, to that of solving a system of six integral equations describing the stress-strain state of the medium. An algorithm for solving the system is given, which can be used in the case when the cavity has a relatively small radius to obtain an approximate solution with any desired degree of accuracy, in the form of an asymptotic expansion. A numerical analysis of the stress-strain state of the elastic medium is given for a wide range of frequencies.