1 A Methodology for the Determination of Dynamic Instabilities in a Car Disc Brake H. Ouyang, J. E. Mottershead, D. J. Brookfield and S. James Department of Engineering, The University of Liverpool, U.K. and M. P. Cartmell Department of Mechanical Engineering, The University of Glasgow, U.K. Abstract: The dynamics of a car disc brake system is investigated by a combined analytical and numerical method. The disc is rotated past the stationary pads and calliper in sliding friction at constant speed. The modal data of the disc are obtained by means of modal testing whereby a dynamic model for the disc is derived based on the thin plate theory. Then the pads, calliper and mounting are analysed by means of the finite element method. Finally the equations of motion for the whole disc brake system is established through the interfaces between the pads and the disc. The stability of the vibrating system is studied by the method of state space. Keywords: parametric vibration, resonance, squeal, instability, car disc brake, pad, calliper, friction, damping, stiffness, finite element method, state space method Nomenclature ab , inner and outer radii of the brake disc. a b ', ' inner and outer radii of the equivalent , thin, annular plate as a substitute for the brake disc. f nodal force vector for pads, calliper and mounting. f o nodal force vector of f less f p . f p nodal force vector for nodes on the pad surfaces in contact with the disc. h thickness of the disc.