Dynamics of a thick-walled spherical casing loaded with a time depending internal pressure

The problem of radial vibration of a thick-walled spherical casing, loaded with an internal pressure, which is a time function, is studied. We assumed that the material of the casing is incompressible. Furthermore, the linear elasticity theory is applied in the considerations. By means of these simplifications, an analytical solution of dynamics of the thick-walled spherical casing loaded with the internal pressure has been obtained. This solution may be used for estimation of strength of spherical ballistic casings which are applied to explosive driven specimen in ring tests. Moreover, the results of this paper contribute to the theory of vibration of continuous engineering systems.