The nonlinear response of a parametrically excited can-tilevered beam is experimentally investigated and nonlinear system identification techniques are used to generate nonlinear modal models to explain the observed behavior. Three techniques are applied to data from simulation of a nonlinear single-mode model as well as from experiments, for a beam which is excited with stationary harmonic input at nearly twice the frequency of the beam's second mode. The first technique 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. Each approach is successful when applied to identify models from simulation data. For the experimental data obtained from a beam under nominally identical conditions, difficulties with using higher harmonic information lead to the incorporation of nonlinear damping terms and an investigation of two-mode behavior. Simulated two-mode behavior demonstrates how the beam's third mode, with natural frequency nearly three times the frequency of the second mode, is excited in the physical structure, thus explaining the mismatch between the previous model and experiment at the third harmonic in the beam's response.
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