Strain growth in spherical explosive chambers subjected to internal blast loading

Spherical pressure vessels are used to fully contain the effects of high explosions. In this paper, the vibrations of a spherical containment vessel undergoing elastic response are investigated. Vibration modes of containment vessels are of particular interest, as it is the superposition and interaction of different modes of response with closely spaced frequencies (beating) that has been reported to be the mechanism of 'strain growth'. The modal frequencies of a complete spherical shell for both axisymmetric and nonaxisymmetric response modes are discussed, based on a sequence of papers that have appeared in the open literature. Analytical predictions are then compared with finite element numerical simulations. It is found that the numerical simulations accurately predict both the axisymmetric and nonaxisymmetric modal frequencies for the complete spherical shell. Next, numerical simulations of modal frequencies for the more complex spherical containment vessel (with nozzles) are compared with the spherical shell results. These simulations for the spherical containment vessel reveal that frequencies are similar to the complete spherical shell, although a splitting of the degenerate frequencies (associated with nonaxisymmetric modes) occurs when progressing from a perfect spherical shell to the containment vessel. As a result, the vibrational response of the spherical containment vessel can be interpreted as a perturbation on the response of a perfect spherical shell. Limited comparisons with experimentally recorded frequencies for participating modes of vessel dynamic response during high explosive containment testing are presented as well. Participating modes potentially capable of beating together to produce 'strain growth' are isolated and are found to agree within 4 percent with frequencies determined from beating frequency measurements. Published by Elsevier Science Ltd.