Application of the modal absorption index (MAI) to reduce the CEA instability over-prediction on a complex frictional system

In complex mechanical systems, frictional contacts can generate undesired unstable vibrations. Contact dynamic instabilities have been the subject of several analyses focused on specific applications. In particular, a large literature can be found on brake squeal. The coalescing of system modes due to the frictional contact is the commonly accepted theory at the origin of most squeal instabilities; Complex Eigenvalue Analysis (CEA) has become a universal tool to evaluate the stability of mechanical systems affected by mode unstable coupling. Nevertheless, the CEA produces an over-prediction of the unstable modes. Recently, an energy approach (MAI index) has been proposed by the authors to identify the mode that absorbs more energy from the frictional interface and results to be unstable in the time response of the system. While the MAI index has been developed and already demonstrated to be effective on a lumped system, the formulation is here extended to a finite element representation of a continuous system.