Differential Equations and Nonlinear Mechanics
Volume 2006 (2006), Article ID 79853, 23 pages
doi:10.1155/DENM/2006/79853
On dynamics and stability of thin periodic cylindrical shells
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.
Abstract
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.