Sensitivity of friction-induced vibration in idealised systems

Friction-induced vibration occurs in many contexts: vehicle brake squeal in particular remains surprisingly unpredictable and poorly understood. Testing theory against measurements has been hindered by the difficulty in obtaining repeatable results suggesting that the phenomenon is sensitive to small changes in parameters. This paper explores highly idealised cases as a starting point to understanding sensitivity. Using a stability criterion based on the roots of the characteristic equations of the system, the sensitivity of predictions to parameter changes is studied, focussing on a single-mode model. The effects of contact stiffness, non-proportional damping and a velocity-dependent coefficient of friction are considered. It is found that each physical effect can significantly alter predictions; each physical effect can lead to extreme sensitivity; and high sensitivity can sometimes occur when modal amplitudes are small such that they might normally be considered insignificant. With a large body of literature focussing on reduced-order models this study provides an important warning when interpreting their results.