Dynamic Stability of a Nonlinear Cylindrical Shell

[+] Author and Article Information
A. Tylikowski

Institute of Machine Design Fundamentals, Warsaw Technical University, Warszawa, Poland 02-524

J. Appl. Mech 51(4), 852-856 (Dec 01, 1984) (5 pages) doi:10.1115/1.3167736 History: Received February 01, 1983; Revised December 01, 1983; Online July 21, 2009


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.

Copyright © 1984 by ASME
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