A FREQUENCY DOMAIN METHOD FOR ESTIMATING THE PARAMETERS OF A NON-LINEAR STRUCTURAL DYNAMIC MODEL THROUGH FEEDBACK

A unifying perspective of non-linear structural dynamic systems as linear in the open loop with non-linear feedback in the closed loop has recently been revisited by the authors. The authors have previously used feedback to derive a new formulation of frequency response function matrices of non-linear systems, which are described as modulations of nominal linear systems. The modulation creates a pseudo-separation of the linear and non-linear dynamics of the system. The present article derives a new method for estimating parameters of non-linear parametric models that uses internal feedback to account for nonlinearities. The main advantage of the new formulation of non-linear system identification is its simplicity. Moreover, the method estimates the linear frequency response matrix and non-linear system parameters at forced and unforced degrees of freedom of general multiple-degree-of-freedom non-linear systems simultaneously. This article demonstrates the implementation of this method on simulated data from single- and multiple-degree-of-freedom lumped parameter models.