Transient Response of an Elastic Medium to Torsional Loads on a Cylindrical Cavity

The transient response of an elastic medium to torsional line loads acting as a step function in time on the surface of an infinite cylindrical bore is obtained. The solution is seen to be composed of a superposition of space-harmonic applied tractions. Integral representations of the resulting displacement and stress fields are derived and numerical results are presented. The behavior in the vicinity immediately behind the outward propagating S-wave fronts is studied and analytic expressions for the resulting singularities and jumps across the fronts are given. These solutions may be used as the Green’s functions for more general spatial loading systems. The response is compared with the known static solution to determine the relative contribution of the transient effect.