Differential Equations and Nonlinear Mechanics
Volume 2006 (2006), Article ID 79853, 23 pages

On dynamics and stability of thin periodic cylindrical shells

Barbara Tomczyk

Department of Structural Mechanics, Technical University of Łódź, Al. Politechniki 6, Łódź 90-924, Poland

Received 29 December 2005; Revised 28 May 2006; Accepted 30 May 2006

Copyright © 2006 Barbara Tomczyk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The object of considerations is a thin linear-elastic cylindrical shell having a periodic structure along one direction tangent to the shell midsurface. The aim of this paper is to propose a new averaged nonasymptotic model of such shells, which makes it possible to investigate free and forced vibrations, parametric vibrations, and dynamical stability of the shells under consideration. As a tool of modeling we will apply the tolerance averaging technique. The resulting equations have constant coefficients in the periodicity direction. Moreover, in contrast with models obtained by the known asymptotic homogenization technique, the proposed one makes it possible to describe the effect of the period length on the overall shell behavior, called a length-scale effect.