Estimation of the periodic solutions of geometrically nonlinear structures by broadband excitation

This paper proposes a methodology for indirectly estimating the periodic solutions of geometrically nonlinear structures using broadband excitation and nonlinear state-space modeling. The methodology is well-suited for thin-walled structures under large amplitude oscillations, and offers a valuable alternative to traditional harmonic-based methods, particularly in situations where such measurements are impractical or difficult to obtain. It relies first on the identification of the reduced-order nonlinear state-space model of the structure under broadband excitation, using the Modal-NSI (Nonlinear Subspace Identification) method. Then, the periodic solutions are studied by merging the Modal-NSI framework with the Harmonic Balance Method (HBM). A continuation technique is adopted to construct the Nonlinear Frequency Response Curves (NFRCs) of the structure, and a monodromy-based stability analysis is developed. The proposed methodology is validated on an experimental thin beam exhibiting a distributed geometrical nonlinearity.