Coupling of systems with nonlinear joints using nonlinear normal modes

The study of a coupled system can be approached using substructuring techniques to reduce the complexity of the problem. The object of this paper is to use these methods for the analysis of a coupled system when nonlinearities are present, since they can deeply affect the computational burden if a finite element method is employed. The idea is to perform a modal reduction analysis using the nonlinear normal modes (NNMs) of each subcomponent and infer the dynamics of the coupled system computing its NNMs. Following this procedure, it is possible to have an insight of the behaviour of a very complex system without performing time consuming analyses. Nonlinearities can be considered either as lumped parameters, if they are localised in a specific area, or as a distributed property, allowing to extend the study for continuous systems, as beams. However, the use of lumped nonlinearities, such as in the stiffness, might be effective if considering two structures that interact through a nonlinear interface, as it happens for joints.