An evaluation of three techniques for system identification of modes in nonlinear structures

Three system identification techniques are described and applied to Loth numerical and experimental data. The experimental data are measurements of a cantilever beam's motion when the response is predominantly that of the second mode of the beam. Both external and parametric excitation of this mode are studied. The first system identification 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 the amplitude and phase modulation equations resulting from a multiple time scales analysis. Simulations are used to explore the excitation necessary for accurate parameter estimation, to understand the effects: of tho measurement process (sampling, filtering, noise) on the parameter estimation, and to help explain the differences between the experimental and theoretical results. There are limitations because of the practicalities of the measurements (continuous-time), and approximations in the theory (multiple time scales and harmonic balance). In general parameter estimates improve as excitation level increases, until the response violates the assumptions that form the theoretical basis of the system identification method.