Nonlinear frequency response curves estimation and stability analysis of randomly excited systems in the subspace framework

In this paper, the periodic solutions of nonlinear mechanical systems are studied starting from the nonlinear state-space model estimated using the nonlinear subspace identification (NSI) technique. In its standard form, NSI needs the input–output data from a nonlinear structure undergoing broadband excitation and requires the prior knowledge of the locations and kind of nonlinearities to be estimated. The method allows the estimation of the nonlinear features of the system and the indirect study of its periodic solutions using a single broadband excitation, without the need of feedback control loops. To this end, the nonlinear frequency response curves of the system are estimated merging the harmonic balance method with the NSI technique and using a continuation approach. Then, a monodromy-based stability analysis is developed in the nonlinear state-space framework to study the stability of the periodic solutions of the system and to track its bifurcations. The method is validated considering conservative nonlinearities on two numerical examples and one experimental application, the latter comprising a double-well oscillator with period-doubling phenomena. The effects of noise and nonlinear modeling errors are also evaluated.