Optimal normal load variation in wedge-shaped Coulomb dampers

Wedge-shaped frictional dampers are widely used in civil, mechanical and aeronautical engineering with the purpose to limit and damp vibrations, increase component fatigue life, or resist seismic loads. The wedge shape induces normal load variations which complicates the analysis. Here, we study a model which can be considered a generalization of the Griffin model, originally devised for underplatform dampers in turbine blade attachments. The model has a mass element (the body whose vibrations are to be damped) linked to the wall by means of a spring and to a massless Coulomb damper via a "contact stiffness". In Griffin's work the normal load acting on the Coulomb damper was kept constant. We introduce cyclic amplitude of the normal load, and phase shift between tangential and normal load. It is found that the optimization curves maintain the minimum for the mean normal load expected by Griffin's model. However, a lower vibration amplitude is found for in-phase loading with respect to the constant load, over the entire frequency range. When the "contact stiffness" is higher than the structure stiffness (as it is generally expected), the maximum vibration decrement for in-phase loading is around 40%.