The Jump-Off Velocity of an Impulsively Loaded Spherical Shell
We consider a constant temperature spherical shell of isotropic, homogeneous, linearly elastic material with density ρ and Lamé coefficients λ and μ. The inner and outer radii of the shell are r i and r o , respectively. We assume that the inside of the shell is a void. On the outside of the shell, we apply a uniform, time-varying pressure p(t). We also assume that the shell is initially at rest. We want to compute the jump-off time and velocity of the pressure wave, which are the first time after t = 0 at which the pressure wave from the outer surface reaches the inner surface. This analysis computes the jump-off velocity and time for both compressible and incompressible materials. This differs substantially from [3], where only incompressible materials are considered. We will consider the behavior of an impulsively loaded, exponentially decaying pressure wave p(t) = P 0 e -αt , where α ≥ 0. We notice that a constant pressure wave P(t) = P 0 is a special case (α = 0) of a decaying pressure wave. Both of these boundary conditions are considered in [3].