Identifying Nonlinear Parameters for Reduced Order Models. Part I: An Analytical Comparison

Assembling nonlinear dynamic models of structures is the goal of numerous research and development organizations. Such a predictive capability is required for the development of advanced, high-performance aircraft structures. Specifically, the ability to predict the response of complex structures to aero-acoustic loading has long been a United States Air Force (USAF) goal. Sonic fatigue has plagued the Air Force since the advent and adoption of the aircraft turbine engine. While the sonic fatigue problem has historically been a maintenance one, predicting nonlinear dynamic response is crucial for future aerospace vehicles. Decades have been spent investigating the dynamic response and untimely failures of aircraft structures, yet little work has been accomplished towards developing practical nonlinear prediction tools. The aim of this paper and a companion one is to present a novel means of assembling nonlinear reduced order models using experimental data and an analytical basis. This paper (Part I) outlines a unique extension of a recently introduced nonlinear identification method; Nonlinear Identification through Feedback of the Outputs (NIFO). The novel extension, or the modal NIFO method, allows for a ready means of identifying nonlinear parameters in reduced order space using measured data. The nonlinear parameters are then used in the assembly of reduced order models, thus providing researchers with a means of conducting predictive studies prior to expensive and questionable experimental efforts. In this paper, an analytical experiment is conducted, using the results from a dynamic nonlinear Finite Element (FE) model, demonstrating the practicality of the method in generating useful nonlinear reduced order models. Nonlinear stiffness parameters were successfully identified for a multiple degree-offreedom (MDOF) nonlinear reduced order model. The nonlinear coefficients compare well with previously published analytical studies of the beam.