Generation of SH-type motion by torsion-free sources

Abstract

The problem of a spherical cavity in an infinite medium is re-examined. The spectral displacement and stress fields are derived when arbitrary tractions are prescribed over the surface of the cavity. This also yields the solution of the problem of the release of pre-existing stress within a spherical zone. The particular case when the radius of the cavity is small in comparison with the wavelength under consideration is discussed in detail. The nature of the tractions is obtained which, when applied at the surface of the cavity, yield the same displacement field as radiated by various point sources. Equivalent body forces are obtained for the release of pre-existing tensile and shear stresses within a spherical zone of small radius. In the course of the analysis, it is shown that an apparently torsion-free source is capable of generating SH-type motion.