Analysis of Motion Resisted by Friction. I. Constant Coulomb and Linear/Coulomb Friction

An exact method for analysis of the transient and steady-state response of harmonically excited frictional oscillators is presented. This method does not postulate antiperiodic type of motion. The method is used to analyze the motion of the constant Coulomb oscillator, under the following conditions: (a) transient conditions; (b) steady-state conditions in the region of multiple stops per cycle and in the presence of viscous damping, where it is shown that viscous damping tends to reduce the number of stops; and (c) at degenerate values of the ratio of driving frequency to natural frequency, where it is shown that unsymmetric motion with only one stop per cycle exists. Furtherfore, the method is applied in analysis of the motion of a linear/Coulomb oscillator, in the region of multiple stops per cycle.