Dynamic instability of a thin circular plate with friction interface and its application to disc brake squeal

The mathematical formulation for determining the dynamic instability due to transverse doublet modes in the self-excited vibration of a thin annular plate is presented in this paper. An analytical approach is developed to obtain the stability results from the eigenvalue problem of a stationary disc with a finite contact area. The approach uses the eigenfunctions of transverse doublet modes in classical plate theory and establishes the formulation of modal instability due to the modal-interaction of a doublet mode pair. The one-doublet mode model of a disc and a discrete model equivalent to the one-doublet mode model are proposed for providing a more fundamental understanding of the onset of squeal. The analytical models are validated through a comparison of results from a modal expansion model obtained from finite element component models. Throughout the analytical investigation, the pad arc length is found to be a critical design parameter in controlling squeal propensity.