Approximate estimates of dynamic instability of long circular cylindrical shells under pure bending

Abstract

In this paper we investigate the dynamic instability problems of long circular cylindrical shells subjected to sudden step bending moments. The expressions to predict the critical dynamic moments are derived. The dynamic instability model is established on two basic assumptions. One is the Brazier's deformed kinematic assumption. The other is the dynamic characteristic assumption in which we assume the longitudinal curvature and ovalisation vibrations reach their extreme values simultaneously when the dynamic instability occurs. Thus, the dynamic instability problem is reduced to the solution of two static equilibrium equations and an energy balance equation. The present results show that the dynamic instability of the long circular cylindrical shells occurs at a moment about 80% of the corresponding critical static moment.