Dynamic Stability of a Nonlinear Cylindrical Shell

Abstract

The stability of the undeflected middle surface of a uniform elastic cylindrical shell governed by Kármán’s equations is studied. The shell is being subjected to a time-varying axial compression as well as a uniformly distributed time-varying radial loading. Using the direct Liapunov method sufficient conditions for deterministic asymptotic as well as stochastic stability are obtained. A relation between stability conditions of a linearized problem and that of Kármán’s equations is found. Contrary to the stability theory of nonlinear plates it is established that the linearized problem should be modified to ensure the stability of the nonlinear shell. The case when the shell is governed by the Itô stochastic nonlinear equations is also discussed.