Evaluation of Different Contact Assumptions in the Analysis of Friction-Induced Vibrations Using Dynamic Substructuring†

Dynamic substructuring methods are initially developed for time-invariant systems 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 time-invariant substructures. Mechanical systems, composed of subsystems in relative motion with a sliding interface, can be analyzed using this approach. In previous work, the authors proposed a solution method in the 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. This assumption implies that the perturbation generated by the friction-induced vibration is neglected. In subsequent work, a more realistic contact assumption was considered to account also for the local vibration of the contact point and the geometric nonlinearity due to the elastic deformation. In this paper, a simplification with respect to the realistic contact assumption is introduced, which neglects the angular variation of the direction normal to the contact interface. The simplified approach is advantageous because it is equally able to highlight the occurrence of friction-induced instabilities, and it reduces the computational burden. The results of the substructuring methods using different contact assumptions are compared with those of a reference numerical method to show how the choice of the contact algorithm allows for tackling a wide range of operating conditions, from simple position-dependent problems up to complex friction-induced vibration phenomena.