Jump-Off Velocity of an Impulsively Loaded Spherical Shell.

摘要

We consider a constant temperature spherical shell of isotropic, homogeneous, linearly elastic material with density (rho) and Lame coefficients (lambda) and (mu). The inner and outer radii of the shell are r(sub i) and r(sub 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(sub 0(sup e))(sup -(alpha)t), where (alpha) (ge) 0. We notice that a constant pressure wave P(t) = P(sub 0) is a special case ((alpha) = 0) of a decaying pressure wave. Both of these boundary conditions are considered in (3).