Using NNMs to Evaluate Reduced Order Models of Curved Beam

Abstract

Reduced order modeling of geometrically nonlinear structures has gained significant attention over the recent years due to its ability to reduce detailed finite element models into computationally efficient yet accurate models. The reduced order models (ROMs) generated can be used to compute the nonlinear normal modes (NNMs) of a structure which serve as a metric to determine the accuracy of the reduced order models; if the NNMs are reproduced accurately then the response to various inputs can also be shown to be accurate. A majority of work has been focused on flat structures while relatively few works have focused on curved structures, those that have, suggested that these structures may introduce complexities to the system. This paper will provide a criteria for selecting basis vectors and load amplitudes for generating accurate ROMs for a curved beam, where softening nonlinearity and snap through are significant. Two methods will be considered: implicit condensation and expansion (ICE) and enforced displacements (ED). A framework for mode selection, load scaling factors and model sensitivity testing will be presented in order to accurately compute the NNMs.