Some Aspects of the Analysis of Stick-Slip Vibrations With an Application to Drill Strings

This paper deals with a systematic procedure to calculate periodic solutions of dynamic systems experiencing dry friction. In this first attempt we limit ourselves to 1 and 2 dof autonomous models where a smooth approximation of the discontinuous friction force is applied. Using the simple shooting method with a numerical integration scheme suitable for stiff differential equations in combination with a path following algorithm, branches of periodic solutions can be followed for a varying design variable. This approach proves to work very well and will be the basis for developing a numerical tool to investigate more complex mdof dynamic systems with stick–slip phenomena.