Dynamic substructuring with time variant coupling conditions for the analysis of friction induced vibrations

Dynamic substructuring methods are originally developed for time invariant systems in order to evaluate the dynamic behavior of a complex structure by coupling the component substructures. Sometimes, the component substructures change their position over time affecting the dynamics of the entire structure. This family of problems can be tackled using substructuring techniques by isolating the time dependency in the coupling conditions among the substructures that are time invariant. Mechanical systems, composed by subsystems in relative motion with a sliding interface, can be analyzed using this approach. In previous works the authors proposed a solution method in time and frequency domain using this approach under the assumption that the relative sliding motion at the contact interfaces is a-priori known, at least approximately. The previous assumption implies that the perturbation generated by the friction induced vibration is neglected. In this work the analysis is extended to account for friction induced vibrations in the formulation of the coupling conditions. This extension allows for the investigation of a wider range of operating conditions including also friction induced instabilities