Physical and geometric parameters uncertainty effect on the nonlinear dynamics of cylindrical panels

Resumo

Some physical and geometric characteristics of a structure such as radius, thickness and Young’s might
present, within a small margin of error, a value different from the nominal value considered in the project.
Therefore, the objective of this work is to investigate the influence of the randomness of these characteristics on
the nonlinear dynamic behavior of a simply supported cylindrical panel subjected to a time-dependent loading.

The nonlinear equations of motion of the panel are deduced from its total potential energy and the strain-
displacements relationships proposed by Donnell's nonlinear shallow shell theory. The physical and geometric

parameters mentioned above are inserted individually as random variables in the partial differential equation of
motion and the problem becomes stochastic due to the presence of randomness. Thus, the partial stochastic
equations of motion of the cylindrical panel are discretized by the Galerkin Stochastic method combined with the
Legendre-Chaos Polynomial and integrated over time by the fourth order Runge Kutta method to obtain several
results to forced nonlinear vibrations of the panel for a given load. These results are compared with those obtained
by the Monte Carlo simulation performed with the deterministic equations, showing the Legendre-Chaos
Polynomial as a good tool for obtaining the statistical responses of the present stochastic system without the need
for a sampling process.