Propagation of Waves from a Spherical Surface of Time-Dependent Radius

The dynamic response of an infinite elastic medium to a time-dependent pressure in a spherical cavity is investigated. For a finite length of time, the wall of the cavity is subjected to an ablation process and the radius of the cavity increases monotonically from the initial value a0 to the permanent value b. Polar symmetry is assumed throughout the analysis. Explicit expressions are derived for the radial and the tangential stresses. The analysis is valid for arbitrary ablation rates and cavity pressures. For a constant ablation rate and a constant cavity pressure, the solutions are compared with the corresponding quasistatic results.