Stresses in a Cylinder Subjected to an Internal Shock

Abstract

Hoop stresses due to a moving shock front in a gas filled, thick walled cylinder can be approximated, using vibration theory. The equation of motion can be combined with hoop stress equations to describe the dynamic changes in hoop stress to provide insight into the phenomenon of flexural resonance, which depends on a critical velocity of the shock in the cylinder. At shock velocities below critical, the maximum hoop stress equals one times the static stress, which would be obtained in the pipe wall if the stress was slowly applied. Above the critical velocity, the maximum hoop stress is less than twice the static hoop stress. Near the critical velocity, the hoop stress approximately triples the static stress, as shown in existing experimental data in the literature. The inclusion of structural and fluid damping in the vibration equations describes the stresses, which were experimentally observed. In short, a comprehensive vibration equation is presented in this paper and is compared to available experimental work.