Identification of nonlinear normal modes of engineering structures under broadband forcing

• A new methodology for the identification of nonlinear normal modes (NNMs) is proposed.
• It generalizes the classical linear phase separation testing techniques.
• It exploits broadband data and makes no assumption as to the modal coupling.
• It integrates nonlinear system identification and numerical continuation of periodic solutions.
• It is demonstrated using a numerical cantilever beam possessing a hardening-softening nonlinearity.

The objective of the present paper is to develop a two-step methodology integrating system identification and numerical continuation for the experimental extraction of nonlinear normal modes (NNMs) under broadband forcing. The first step processes acquired input and output data to derive an experimental state-space model of the structure. The second step converts this state-space model into a model in modal space from which NNMs are computed using shooting and pseudo-arclength continuation. The method is demonstrated using noisy synthetic data simulated on a cantilever beam with a hardening-softening nonlinearity at its free end.