Stochastic parametric instability of thin cylindrical shell using various shell theories

The dynamic stability problem is solved for thin cylindrical shells compressed by time-dependent deterministic or stochastic membrane forces using three common thin shell theories, namely Donnell's, Love's and Fliigge's shell theories. The asymptotic stability and almost sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunov's direct method. The present paper compares effects of the use of the various shell theories on the dynamic stability regions.