A time domain approach for identifying nonlinear vibrating structures by subspace methods

Starting from the perspective of nonlinearities as internal feedback forces, a method in the time domain for the identification of nonlinear vibrating structures is described. Although its formulation is very simple, particular care has to be taken to reduce the ill-conditioning of the problem, in order to find numerically stable solutions. To this purpose the robustness and the high numerical performances of the subspace algorithms are successfully exploited, as demonstrated by the implementation of the method on simulated data from single and multi-degree of freedom systems with typical nonlinear characteristics. The method allows to estimate the coefficients of the nonlinearities away from the location of the applied excitations and also to identify the linear dynamic compliance matrix when the number of excitations is smaller than the number of response locations. The results comparison reported in this paper highlights the key advantage of the proposed method: the capability of treating multi-degree of freedom nonlinear systems holding different types of nonlinearities and the capability of selecting non-negligible nonlinear terms, with a light computational effort and with a limited number of time samples.