Locating structural nonlinearities using linear frequency response functions and nonlinear orthogonal projections

This paper addresses the identification of the spatial location of nonlinearities based on classical modal testing. Interpreting nonlinear systems as linear systems with a nonlinear feedback loop shows that the nonlinear contribution to the response and the nonlinear restoring forces are related through the linear frequency response function (FRF) matrix. Specifically, if the nonlinearity is localized, the response’s nonlinear part is intimately linked with the linear FRF at the nonlinearity location. Thus, processing input–output data measured under pseudorandom excitation, the nonlinearity location can be inferred from the comparison of the nonlinear part of the response with the different measured FRFs. A second approach, which provides a direct estimation of the nonlinear restoring forces at the different degrees of freedom, also utilizes the same relations. Both procedures are demonstrated numerically and experimentally.