9322106 Barber Frictional heating of brakes generates thermoelastic instabilities which can result in vibrations at high speed. The phenomenon is particularly pronounced in high performance systems, such as those which currently are under development for automotive uses. Analytical methods for determining critical speeds of hot spot development will be extended from semifinite conditions to the finite dimensions of actual brake systems. The approach assumes exponential growth with time of an initially small perturbation, modifies the problem to an eigenvalue problem in spatial dimension only, and discretizes it by the finite element method. Parallel experiments to validate the results will be run at Allied Signal Corporation's Friction Materials Department. ***