International Journal of Mechanical Sciences 41 (1999) 325—336 Friction-induced vibration of an elastic slider on a vibrating disc H. Ouyang , J.E. Mottershead *, M.P. Cartmell , D.J. Brookfield  Department of Mechanical Engineering, University of Liverpool, Liverpool L69 3GH, England, UK  Department of Mechanical Engineering, University of Glasgow, Glasgow G12 8QQ, Scotland, UK Received 6 August 1997; received in revised form 29 June 1998 Abstract The in-plane vibration of a slider-mass which is driven around the surface of a flexible disc, and the transverse vibration of the disc, are investigated. The disc is taken to be an elastic annular plate and the slider has flexibility and damping in the circumferential (in-plane) and transverse directions. The static friction coefficient is assumed to be higher than the dynamic friction. As a result of the friction force acting between the disc and the slider system, the slider will oscillate in the stick-slip mode in the plane of the disc. The transverse vibration induced by the slider will change the normal force on the disc, which in turn will change the in-plane oscillation of the slider. A numerical method is used to solve the two coupled equations of the motion. Results indicate that normal pressure and rotating speed can drive the system into instability. The rigidity and damping of the disc and transverse stiffness and damping of the slider tend to suppress the vibrations. The in-plane stiffness and damping of the slider do not always have a stabilizing effect. The motivation of this work is the understanding of instability and squeal in physical systems such as car brake discs where there are vibrations induced by non-smooth dry-friction forces.  1998 Elsevier Science Ltd. All rights reserved. Keywords: non-linear vibration; instability; stick-slip; car brake disc; noise Nomenclature a, b inner and outer radii of the annular disc c, c  damping coefficient of the slider in the transverse and in-plane directions h thickness of the disc i !1 k, k  transverse and in-plane stiffness of the slider system m mass of the slider * Corresponding author. 0020-7403/99/$ — see front matter  1998 Elsevier Science Ltd. All rights reserved. PII: S 0 0 2 0 - 7 4 0 3 ( 9 8 ) 0 0 0 5 9 - 9