Energy analysis of contact nonlinear transitions: Insights on the origin of limit cycles and bi-stable states in friction-induced instabilities

This work explores the bi-stable behavior of a frictional system susceptible to mode-coupling instability. The focus is placed on the variations of the energy flows at the contact, due to external perturbations, and the role of contact nonlinearities on the system dynamic response. A lumped parameter numerical model, incorporating contact nonlinearities, is developed, allowing transitions between sliding, sticking, and detachment contact conditions. While prestressed complex eigenvalue analysis (CEA) allows for the identification of instabilities in the linearized frictional system, transient simulations were conducted to investigate the nonlinear system dynamics and the possibility of switching between two stable states (mode coupling or stable sliding) by an external perturbation. The investigation of the bi-stable state has been carried out by performing an energy balance of the system, accounting for the exchanged mechanical energies at the contact, to highlight the key role of contact nonlinearities in driving the power flows at the origin of the different stable states and respective limit cycle. The findings underscore the critical role of contact nonlinearities in shaping the power flows at the contact interface, determining the transition between stable sliding and mode-coupling, and providing further insights into the “fugitive” feature of mode-coupling instabilities.