Friction damping is one of the most exploited systems of passive control of vibration of mechanical systems. A common type of blade-to-blade friction dampers are the so-called underplatform dampers (UPDs); they are metal devices placed under the blade platforms and held in contact with them by the centrifugal force acting during rotation. The effectiveness of underplatform dampers to dissipate energy by friction and reduce vibration amplitude depend mostly on the damper geometry and material and on the static pre-loads pressing the damper against the blade platforms. The common procedure used to estimate the static pre-loads acting on underplatform dampers consists in decoupling the static and the dynamic balance of the damper. A preliminary static analysis of the contact is performed in order to compute the static pressure distribution over the damper/blade interfaces, assuming that it does not change when vibration occurs. In this paper a coupled approach is proposed. The static and the dynamic displacements of blade and underplatform damper are coupled together during the forced response calculation. Both the primary structure (the bladed disk) and the secondary structure (the damper) are modelled by finite elements and linked together by contact elements, allowing for stick, slip and lift off states, placed between each pair of contact nodes, by using a refined version of the state-of-the-art friction contact model. In order to model accurately the blade/damper contact with a large number of contact nodes without increasing proportionally the size of the set of non-linear equations to be solved, damper and blade dynamics are modelled by linear superposition of a truncated series of normal modes. The proposed method is applied to a bladed disk under cyclic symmetric boundary conditions in order to show the capabilities of the method compared to the classical decoupled approaches.

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