Bounded responses from a nonlinear model with mode-coupling instability and negative stiffness in one of its contact interfaces

Mode coupling is a mechanism of friction-induced vibration that is considered one of the most relevant theories for studying brake squeal. This work introduced a negative stiffness effect in one of the contact interfaces from a nonlinear model with two degrees-of-freedom (DOF) and no external sources of damping. The linearized version presented multi-stability, where pure imaginary characteristic roots (i.e., marginal or neutral stability conditions) occurred for two points under specific parameter combinations. Besides, incommensurate natural frequency ratios prevail under those circumstances unless the exact parameter combinations are applied. Thus, an approximated two-frequency solution was developed using the Harmonic Balance Method (HBM) to evaluate which frequencies played the main role on the power exchanged at contact interfaces. The main results show that some of the marginally stable conditions produced quasi-periodic oscillations, where the liquid power exchanged (i.e. due to the oscillation of the system alone) was represented with important contributions of dominant frequency combinations. As a result, the total work exchanged varied in time as a bounded train of pulses.