Stresses in a Cylinder Subjected to an Internal Shock

Hoop stresses due to a moving shock front in either a gas or liquid filled 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 creates pipe stresses significantly in excess of the stresses expected from a slowly applied, or static, pressure loading. To investigate flexural resonance, vibration equations were successfully compared to available experimental results. At shock velocities, the maximum hoop stress is related to a vibration equation for a suddenly applied load. Consideration of structural and fluid damping, as well as pipe constraints at the end of the pipe, were considered in the derivation of the vibration equations. In short, vibration equations are presented in this paper and are compared to available experimental work. The equations describe hoop stresses in a pipe when a step increase in pressure travels the bore of a pipe at sonic or supersonic velocities.