Nonlinear Reduced Order Random Response Analysis of Structures with Shallow Curvature

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures with shallow curvature under random loadings. For reduced order analysis, the modal basis selection must be capable of reflecting the coupling in both the linear and nonlinear stiffness. For the symmetric shallow arch under consideration, four categories of modal basis functions are defined. Modal bases having symmetric transverse displacements and modal bases having anti-symmetric transverse displacements may each be either transverse dominated or in-plane dominated. The response of an aluminum arch under a uniformly distributed transverse random loading is investigated. Results from nonlinear modal simulations made using various modal bases are compared with those obtained from a numerical simulation in physical degrees-of-freedom. While inclusion of transverse dominated modes having a symmetric transverse displacement is important for all response regimes, it is found that the in-plane dominated modes having a symmetric transverse displacement become increasingly important in the nonlinear response regime. In the autoparametric response regime, the inclusion of both transverse and in-plane dominated modes, each with an anti-symmetric transverse displacement distribution, is found to be critical.