A perturbation analysis of nonlinear squeal vibrations in aircraft braking systems is presented. The multiple-time-scale technique is used to obtain equations for the limit cycle amplitude and frequency of general autonomous self-excited systems with Coulomb friction, nonlinear stiffness and damping. Coulomb friction terms are shown to modify the amplitude equation to yield perturbations and a universal unfolding of the fundamental Hopf pitchfork bifurcation. The solution method is applied to a nonlinear squeal model in which nonlinear mechanical and material properties of the brake heat stack produce the destabilizing mechanism. The analysis shows that stable and unstable limit cycles can exist for a given constant brake friction coefficient.

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