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Mathematical Problems in Engineering
Volume 2015, Article ID 758959, 18 pages
Research Article

Influence of Physical and Geometrical Uncertainties in the Parametric Instability Load of an Axially Excited Cylindrical Shell

1School of Civil Engineering, Federal University of Goiás, Avenida Universitária, 1488, Setor Universitário, 74605-220 Goiás, GO, Brazil
2Department of Civil Engineering, Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Rua Marquês de São Vicente 225, 22451-900 Gávea, RJ, Brazil

Received 10 October 2014; Accepted 24 February 2015

Academic Editor: Huaguang Zhang

Copyright © 2015 Frederico Martins Alves da Silva 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.


This work investigates the influence of Young’s modulus, shells thickness, and geometrical imperfection uncertainties on the parametric instability loads of simply supported axially excited cylindrical shells. The Donnell nonlinear shallow shell theory is used for the displacement field of the cylindrical shell and the parameters under investigation are considered as uncertain parameters with a known probability density function in the equilibrium equation. The uncertainties are discretized as Hermite-Chaos polynomials together with the Galerkin stochastic procedure that discretizes the stochastic equation in a set of deterministic equations of motion. Then, a general expression for the transversal displacement is obtained by a perturbation procedure which identifies all nonlinear modes that couple with the linear modes. So, a particular solution is selected which ensures the convergence of the response up to very large deflections. Applying the standard Galerkin method, a discrete system in time domain that considers the uncertainties is obtained and solved by fourth-order Runge-Kutta method. Several numerical strategies are used to study the nonlinear behavior of the shell considering the uncertainties in the parameters. Special attention is given to the influence of the uncertainties on the parametric instability and time response, showing that the Hermite-Chaos polynomial is a good numerical tool.