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

Abstract

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.

Análise do comportamento dinâmico de um sistema mecânico sujeito a bifurcação instável

“…Research, Society and Development, v. 9, n. 7, e424973763, 2020 (CC BY 4.0) | ISSN 2525-3409 | DOI: http://dx.doi.org/10.33448/rsd-v9i7.3763 5 Seguindo a mesma linha de pesquisa Silva, Brazão & Gonçalves (2015) investigaram a influência de incertezas nos parâmetros físicos e geométricos para a determinação da carga de instabilidade paramétrica de uma casca cilíndrica excitada axialmente, utilizando o método de Galerkin Estocástico juntamente com o polinômio de Hermite-Caos. A incerteza é considerada inicialmente em apenas um de seus parâmetros: no módulo de elasticidade, na espessura e na amplitude da imperfeição geométrica inicial.…”

Nonlinear Vibration of the Blade with Variable Thickness

“…e stress, deformation, and snap-through conditions of thin, axisymmetric, shallow bimetallic shells were investigated by Jakomin and Kosel [25]. da Silva et al [26] studied the influence of Young's modulus, shell thickness, and geometrical imperfection uncertainties on the parametric instability loads of simply supported axially excited cylindrical shells. Li et al [27] had a research on the free vibration of the stiffened cylindrical shell with general boundary conditions.…”

Stochastic Natural Vibration Analyses of Free-Form Shells

“…However, the existing work mainly studies static characteristics and it is limited to the deterministic analysis without any consideration of uncertainty factors, which are unavoidable in practical engineering, such as geometrical imperfection and deviations of material properties. The previous stochastic studies on traditional shells have demonstrated the significant effect of uncertain factors on mechanical properties of structures [9][10][11][12][13]. The construction process of free-form shells is more complex when compared with traditional shells, which tends to lead more uncertainty factors.…”