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

• Published in: Mathematical problems in engineering Vol. 2015; no. 2015; pp. 1 - 18
• Main Authors: Silva, Frederico Martins Alves da, Gonçalves, Paulo Batista, Brazão, Augusta Finotti
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2015; Hindawi Limited
• Subjects: Chaos theory; Civil engineering; Cylindrical shells; Discrete systems; Engineering; Equations of motion; Equilibrium equations; Galerkin method; Galerkin methods; Hermite polynomials; Instability; Load; Mathematical analysis; Mathematical models; Modulus of elasticity; Motion stability; Nonlinear response; Nonlinearity; Parameter identification; Parameter uncertainty; Polynomials; Probability density functions; Runge-Kutta method; Shallow shells; Shell stability; Shell theory; Stability; Time domain analysis; Time response; Uncertainty; Brazil
• ISSN: 1024-123X; 1563-5147
• DOI: 10.1155/2015/758959

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.