A ring damper can be affixed to a rotating base structure such as a gear, an automotive brake rotor or a gas turbine's labyrinth air seal. Depending on the frequency range, wavenumber and level of preload, vibration of the base structure can be effectively and passively attenuated by friction that develops along the interface between it and the damper. The assembly is modelled as two rods that couple in longitudinal vibration through spatially distributed hysteretic friction, with each rod having periodic boundary conditions in a manner analogous to an unwrapped ring and disc. As is representative of rotating machinery applications, the system is driven by a travelling wave disturbance, and for that form of excitation, the base structure's and the damper's responses are determined without the need for computationally intensive simulation. The damper's performance can be optimized with respect to normal preload, and its effectiveness is insensitive to variations in preload or the excitation's magnitude when its natural frequency is substantially lower than the base structure's in the absence of contact.