A hybrid frequency response function formulation for MDOF nonlinear systems

This paper introduces a hybrid technique for formulation of frequency response functions (FRFs) for nonlinear MDOF systems, based on the Structural modification using frequency response function (SMURF) technique. The technique can produce FRFs at the desired coordinates on the structure. The term “hybrid” indicates that the underlying linear system is reduced by expressing it in FRF form, while the nonlinearities are treated in the form of describing functions based on spatial elements. The method uses several FRFs instead of the spatial model therefore it is characterized by lower computational costs. Moreover, the experimentally measured FRFs of the underlying linear structure can be applied in this technique. A system with cubic stiffness and friction damping nonlinearities is used as a numerical case study to verify the proposed technique.