Friction-induced vibration and stick-slip waves

This paper presents a short review and new results about the self-excited responses under the form of stick-slip regimes. First, the Van-der Pol oscillator with one degree of freedom is considered. Then it is shown that it is possible to build semi-analytical and numerical (by the FEM.) solutions of stick-slip-separation waves for a brake-like system. Then, we present new results concerning the mechanical model composed of a rigid half space in frictional sliding with an elastic half-space. The method of solution, based on periodic complex Radoks potentials, is novel and differs from those in literature. Besides, in contrast with many works, we shall consider the longitudinal elongation which plays a crucial rule in the solution procedure. A unique and weakly singular solution is found and satisfies all stick-slip conditions except over a narrow zone at transition points which implies a cracklike behaviour at the stick-slip borders.