Identification of nonlinear parameters for reduced order models

Constructing nonlinear structural dynamic models is a goal for numerous research and development organizations. Such a predictive capability is required in the development of advanced, high-performance aircraft structures. Specifically, the ability to predict the response of complex structures to engine induced and aero acoustic loading has long been a United States Air Force (USAF) goal. Sonic fatigue has plagued the USAF since the advent and adoption of the turbine engine. While the problem has historically been a maintenance one, predicting the dynamic response is crucial for future aerospace vehicles. Decades have been spent investigating the dynamic response and untimely failure of aircraft structures, yet little work has been accomplished towards developing practical nonlinear prediction methods. Further, the last decade has witnessed an appreciable amount of work in the area of nonlinear parameter identification. This paper outlines a unique and important extension of a recently introduced nonlinear identification method: Nonlinear Identification through Feedback of the Outputs (NIFO). The novel extension allows for a ready means of identifying nonlinear parameters in reduced order space using experimental 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. This paper details both an analytical and experimental study conducted on a well-characterized clamped–clamped beam subjected to broadband random loading. Amplitude dependent, constant stiffness parameters were successfully identified for a multiple-degree-of-freedom (MDOF) nonlinear reduced order model. The nonlinear coefficients identified from the analytical scenario compare well with previously published studies of the beam. Nonlinear parameters were also successfully identified from the raw experimental data. Finally, a MDOF nonlinear reduced order model, constructed from experimental data, was used to predict the experimental response of the beam to other loading conditions. Beam response spectra and average displacement values from the prediction model also compare well with the experimental results.