Disc brake squeal is a manifestation of the friction-induced self-excited instability of the brake system. One of known techniques in suppressing dynamic instabilities in nonlinear systems is by applying dither. The focus of this paper is to examine, through numerical examples, the feasibility and effects of dither on nonlinear systems as a means of quenching large-amplitude limit cycles. In particular, various ways of introducing the dither, either via modifications of the system characteristics or as external excitation, are explored. The investigation is extended to a disc brake system using finite elements simulations. Numerical results show that large-amplitude vibrations can be suppressed by dither and careful tuning of the amplitude and frequency of the dither can result in an effective quenching. The potential application of this technique to disc brake squeal control is also discussed.