Differential Equations and Nonlinear Mechanics
Volume 2006 (2006), Article ID 59709, 8 pages

Dynamics of flexible shells and Sharkovskiy's periodicity

Vadim A. Krysko,1 Jan Awrejcewicz,2 Natalya E. Saveleva,1 and Anton V. Krysko1

1Department of Mathematics, Saratov University, Saratov 410054, Russia
2Department of Automatics and Biomechanics, Technical University of Łódź, 1/15 Stefanowskiego Street, Łódź 90-924, Poland

Received 15 December 2005; Revised 6 June 2006; Accepted 14 June 2006

Copyright © 2006 Vadim A. Krysko et al. 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.


Complex vibration of flexible elastic shells subjected to transversal and sign-changeable local load in the frame of nonlinear classical theory is studied. A transition from partial to ordinary differential equations is carried out using the higher-order Bubnov-Galerkin approach. Numerical analysis is performed applying theoretical background of nonlinear dynamics and qualitative theory of differential equations. Mainly the so-called Sharkovskiy periodicity is studied.