DYNAMIC SURFACE SOLUTIONS IN LINEAR ELASTICITY AND VISCOELASTICITY WITH FRICTIONAL BOUNDARY-CONDITIONS

This paper presents a study on the dynamic stability of the steady fri ctional sliding of a linear elastic or viscoelastic half-space compres sed against a rigid plane which moves with a prescribed nonvanishing t angential speed. The system of differential equations and boundary con ditions that govern the small plane oscillations of the body about the steady-sliding state of deformation is established. It is shown that for large coefficient of friction and large Poisson's ratio the steady -sliding of the elastic body is dynamically unstable. This instability manifests itself by growing surface oscillations which necessarily pr opagate from front to rear and which in a short time lead to situation s of loss of contact or stick. Similarly to what has been found with v arious finite dimensional frictional systems, these flutter type surfa ce instabilities result from the intrinsic nonsymmetry of dry friction contact laws. The effect of viscous dissipation within the deformable body is also assessed: when viscous dissipation is present larger coe fficients of friction are required for the occurrence of surface solut ions propagating and growing from front to rear.