Stochastic Reduced Order Models for Uncertain Infinite-Dimensional Geometrically Nonlinear Dynamical Systems- Stochastic Excitation Cases

The application of the nonparametric stochastic modeling technique to reduced order models of geometrically nonlinear structures recently proposed is here further demonstrated. The complete methodology: selection of the basis functions, determination and validation of the mean reduced order model, and introduction of uncertainty is first briefly reviewed. Then, it is applied to a cantilevered beam to study the effects of uncertainty on its response to a combined loading composed of a static inplane load and a stochastic transverse excitation representative of earthquake ground motions. The analysis carried out using a 7-mode reduced order model permits the efficient determination of the probability density function of the buckling load and of the uncertainty bands on the power spectral densities of the stochastic response, transverse and inplane, of the various points of the structure.