Repeated-root modes of a disc rotor in a closed-loop coupling model

To develop closed-loop coupling models for brake squeal analyses, the modal parameters of the disc rotor are calculated from the finite element model and many repeated-root modes appear. A pair of repeated-root modes represents one vibration mode. However, the current substructure mode composition analysis method treats each pair of repeated-root modes as two independent modes, so there may be difficulty in identifying the most important parameters for the noise mode. The modal shape coefficients of the repeated-root modes are fit from the finite element results. A single composition factor is then derived for each pair of repeated-root modes which represents the total contribution of these modes to the noise mode according to the definition of the mode composition and the curve fits. Examples show that this method more clearly relates repeated-root modes of the disc rotor to the noise mode, which provides support for developing effective measures for squeal reduction.