| A ring damper system is affixed to a base structure in order to passively control its vibration. Applications of ring dampers include automotive brake rotors and drums, labyrinth air seals in gas turbine engines, and power transmission gearing. This thesis examines friction damping in a continuous ring damper, and its base structure, in the context of three models at different levels of sophistication---mono-coupled and mutually-coupled rod models, and a more general finite element model. The damper and base structures each have periodic boundary conditions in a manner conceptually analogous to an "unwrapped" ring and disk, and they are in frictional contact at an arbitrary number of locations. As is representative of the motivating rotating machinery applications, each system is excited by a traveling wave disturbance. The harmonic balance method is applied to determine the steady-state response amplitude during sticking/slipping motions at the interface. Irrespective of the number of elements or contact points in the analysis, the response of the base/damper system is determined directly from a set of nonlinear algebraic equations without the need for computationally-intensive simulation. The mutually-coupled rod model treats dynamic coupling between the base and the damper, and it is suitable for situations in which the base and the damper are of similar mass. When the damper is light compared to the base subsystem, as is often the case in practice, and when the excitation frequency is well-separated from the base's natural frequency, the simpler mono-coupled model can alternatively be used. The finite element model is applicable to the in-plane and out-of-plane vibration of more general axisymmetric structures with distributed friction. In that model, the order of the equation of motion of each substructure is reduced to the number of nodal degrees of freedom through the use of a propagation constant phase shift. The finite element model is not only computationally efficient, but it can also serve as a point of comparison for the development of computational methods for frictionally-coupled vibration problems. The models are used to optimize the design of the ring damper with respect to preload, excitation amplitude and frequency, and mass, stiffness, and natural frequency ratios between the damper and the base. The effectiveness of the damper is less sensitive to variations in the preload, or the excitation's magnitude, when its natural frequency is substantially lower than that of the base in the absence of contact, and also when it is well-separated from the excitation frequency. |
