Rotating Slip Stick Separation Waves

We consider a thick-walled elastic tube (cylinder) which is fixed in space at its outer surface. Inside the tube a rigid shaft rotates about the common axis of the tube-shaft system. The inner diameter of the tube is assumed to be smaller than the outer diameter of the shaft. Hence the tube is compressed. The tangential contact force is assumed to be given by Coulomb’s law of dry friction. For the infinite dimensional continuous tube shaft system solutions are found, which are rotating slip-stick and slip-stick-separation waves with different wave numbers. To understand some special features of these solutions we also consider a simple one degree of freedom oscillator, however, with a more complicated dry friction contact force which now depends on the relative velocity possessing a decreasing and increasing part.