Evaluation of Geometrically Nonlinear Reduced-Order Models with Nonlinear Normal Modes

Several reduced-order modeling strategies have been developed to create low-order models of geometrically nonlinear structures from detailed finite element models, allowing one to compute the dynamic response of the structure at a dramatically reduced cost. However, the parameters of these reduced-order models are estimated by applying a series of static loads to the finite element model, and the quality of the reduced-order model can be highly sensitive to the amplitudes of the static load cases used and to the type/number of modes used in the basis. This paper proposes to combine reduced-order modeling and numerical continuation to estimate the nonlinear normal modes of geometrically nonlinear finite element models. Not only does this make it possible to compute the nonlinear normal modes far more quickly than existing approaches, but the nonlinear normal modes are also shown to be an excellent metric by which the quality of the reduced-order model can be assessed. Hence, the second contribution of this work is to demonstrate how nonlinear normal modes can be used as a metric by which nonlinear reduced-order models can be compared. Various reduced-order models with hardening nonlinearities are compared for two different structures to demonstrate these concepts: a clamped-clamped beam model, and a more complicated finite element model of an exhaust panel cover.