Harmonic Response of Smoothly Embedded Rigid Sphere

Abstract

The category of problems that examines the dynamic behavior of inclusions embedded in elastic media is of particular interest to the study of dynamic soil‐structure interaction. In a majority of investigations, the interface between the inclusion and the surrounding elastic medium is assumed to be perfectly bonded. This paper examines the elastodynamic problem pertaining to the steady rectilinear oscillations of a spherical rigid inclusion that is embedded in smooth bilateral contact with an isotropic elastic medium of infinite extent. The bilateral contact is maintained by the application of a uniform radial stress field at infinity. The inclusion is subjected to a harmonic oscillation. The analytical solution for the resulting elastodynamic problem is developed in exact closed form. The numerical results presented in the paper illustrate the manner in which the dynamic compliance of the embedded rigid spherical inclusion is influenced by the frictionless boundary conditions at the inclusion‐elastic medium interface.