Analysis of friction induced mode coupling instabilities using dynamic substructuring

In complex vibrating systems, contact and friction forces can produce a dynamic response of the system (friction induced vibrations). They can arise when different parts of the system move one with respect to the other generating friction force at the contact interface. Component mode synthesis and more in general substructuring techniques represent a useful and widespread tool to investigate the dynamic behavior of complex systems, but classical techniques require that the component subsystems and the coupling conditions (compatibility of displacements and equilibrium of forces) are time invariant. In previous papers, it was shown that contact problems can be cast in the framework of dynamic substructuring by considering the models of the component substructures as time invariant, while the coupling conditions must be time dependent. In this paper a substructuring method is proposed that, depending on the contact assumption, is able either to account only for the macroscopic sliding between substructures, or to consider also the local vibrations of the contact points or to consider also the geometric nonlinearity due to the elastic deformation. This allows to adapt the contact algorithm to the contact problem that must be tackled, i.e. position dependent dynamics or friction induced vibrations.