System identification of modes in nonlinear structures

Nonlinear system identification techniques are formulated to generate models of modes in physical structures. Three techniques are described: the first is based on the continuous-time differential equation model of the system, the second uses relationships generated by the method of harmonic balance, and the third is based on fitting steady-state response data to steady-state amplitude and phase predictions resulting from a multiple time scales analysis. The methods are applied to simulation data from a theoretical nonlinear model to determine how to optimize the data set to improve parameter estimation. A system identification philosophy is described that combines simulations and experiments to understand how to test particular structures and improve models with structural deficiencies. The methods are then applied to simulated and experimental models of modes of a cantilevered beam in two configurations: where the excitation enters the model externally, and where the excitation enters the model parametrically. The beam is excited with stationary sinusoids which excite steady-state harmonic responses around the second mode of the beam. While each method is successful when applied to identify models for simulated systems, difficulties with using higher harmonic information from experimental data lead to the incorporation of nonlinear damping terms and an investigation of two-mode behavior. Multi-mode behavior is found to explain the mismatch between the model and experiment at the third harmonic in beam\u27s responses. Methods are described for applying the system identification techniques on multi-mode systems. As an alternative to steady-state testing, the continuous time based method of system identification is applied to the cantilever beam externally excited with a swept sine. The considerably shorter test times are shown to produce estimates that are comparable to the estimates from steady-state test data